DSpace Collection: Volume 30 Number 2-3
http://hdl.handle.net/10525/1730
Serdica Mathematical Journal Volume 30, Number 2-3, 2004The Collection's search engineSearch the Channelsearch
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Binomial Skew Polynomial Rings, Artin-Schelter Regularity, and Binomial Solutions of the Yang-Baxter Equation
http://hdl.handle.net/10525/1747
Title: Binomial Skew Polynomial Rings, Artin-Schelter Regularity, and Binomial Solutions of the Yang-Baxter Equation<br/><br/>Authors: Gateva-Ivanova, Tatiana<br/><br/>Abstract: Let k be a field and X be a set of n elements. We introduce and study a class of quadratic k-algebras called quantum binomial algebras.Our main result shows that such an algebra A defines a solution of the classical Yang-Baxter equation (YBE), if and only if its Koszul dual A!is Frobenius of dimension n, with a regular socle and for each x, y ∈ X an equality of the type xyy = αzzt, where α ∈ k \{0}, and z, t ∈ X is satisfied in A. We prove the equivalence of the notions a binomial skew polynomial ring and a binomial solution of YBE. This implies that the Yang-Baxter algebra of such a solution is of Poincaré-Birkhoff-Witt type, and possesses a number of other nice properties such as being Koszul, Noetherian, and an Artin-Schelter regular domain.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 81R50, 16W50, 16S36, 16S37.Remarks on the Nagata Conjecture
http://hdl.handle.net/10525/1746
Title: Remarks on the Nagata Conjecture<br/><br/>Authors: Strycharz-Szemberg, Beata; Szemberg, Tomasz<br/><br/>Abstract: The famous Nagata Conjecture predicts the lowest degree ofa plane curve passing with prescribed multiplicities through given pointsin general position. We explain how this conjecture extends naturally viamultiple point Seshadri constants to ample line bundles on arbitrary surfaces.We show that if there exist curves of unpredictable low degree, then theymust have equal multiplicities in all but possibly one of the given points.We use this restriction in order to obtain lower bounds on multiple pointSeshadri constants on a surface. We discuss also briefly a seemingly newpoint of view on the Nagata Conjecture via the bigness of the involvedlinear series.<br/><br/>Description: 2000 Mathematics Subject Classification: 14C20, 14E25, 14J26.Invariants of Unipotent Transformations Acting on Noetherian Relatively Free Algebras
http://hdl.handle.net/10525/1745
Title: Invariants of Unipotent Transformations Acting on Noetherian Relatively Free Algebras<br/><br/>Authors: Drensky, Vesselin<br/><br/>Abstract: The classical theorem of Weitzenböck states that the algebra of invariants K[X]^g of a single unipotent transformation g ∈ GLm(K) acting on the polynomial algebra K[X] = K[x1, . . . , xm] over a field K of characteristic 0 is finitely generated.<br/><br/>Description: 2000 Mathematics Subject Classification: 16R10, 16R30.Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory
http://hdl.handle.net/10525/1744
Title: Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory<br/><br/>Authors: Chipchakov, I.<br/><br/>Abstract: This paper gives a characterization of Henselian discrete valuedfields whose finite abelian extensions are uniquely determined by their normgroups and related essentially in the same way as in the classical local classfield theory. It determines the structure of the Brauer groups and charactergroups of Henselian discrete valued strictly primary quasilocal (or PQL-) fields, and thereby, describes the forms of the local reciprocity law for such fields. It shows that, in contrast to the special cases of local fieldsor strictly PQL-fields algebraic over a given global field, the norm groupsof finite separable extensions of the considered fields are not necessarilyequal to norm groups of finite Galois extensions with Galois groups of easilyaccessible structure.<br/><br/>Description: 2000 Mathematics Subject Classification: 11S31 12E15 12F10 12J20.Linearly Normal Curves in P^n
http://hdl.handle.net/10525/1743
Title: Linearly Normal Curves in P^n<br/><br/>Authors: Pasarescu, Ovidiu<br/><br/>Abstract: We construct linearly normal curves covering a big range from P^n, n ≥ 6 (Theorems 1.7, 1.9). The problem of existence of such algebraic curves in P^3 has been solved in [4], and extended to P^4 and P^5 in [10]. In both these papers is used the idea appearing in [4] and consisting in adding hyperplane sections to the curves constructed in [6] (for P^3) and [15, 11] (for P^4 and P^5) on some special surfaces. In the present paper we apply the same idea to the curves lying on some rational surfaces from P^n, constructed in [12, 3, 2] (see [13, 14] also).<br/><br/>Description: 2000 Mathematics Subject Classification: 14H45, 14H50, 14J26.Kneser and Hereditarily Kneser Subgroups of a Profinite Group
http://hdl.handle.net/10525/1742
Title: Kneser and Hereditarily Kneser Subgroups of a Profinite Group<br/><br/>Authors: Basarab, Şerban<br/><br/>Abstract: Given a profinite group Γ acting continuously on a discrete quasi-cyclic group A, certain classes of closed subgroups of Γ (radical, hereditarily radical, Kneser, almost Kneser, and hereditarily Kneser) having natural field theoretic interpretations are defined and investigated. One proves that the hereditarily Kneser subgroups of Γ form a closed subspace of the irreducible spectral space of all closed subgroups of Γ, and a hereditarily Kneser criterion for hereditarily radical subgroups is provided.<br/><br/>Description: 2000 Mathematics Subject Classification: 20E18, 12G05, 12F10, 12F99.Minimal Codewords in Linear Codes
http://hdl.handle.net/10525/1741
Title: Minimal Codewords in Linear Codes<br/><br/>Authors: Borissov, Yuri; Manev, Nickolai<br/><br/>Abstract: Cyclic binary codes C of block length n = 2^m − 1 and generator polynomial g(x) = m1(x)m2^s+1(x), (s, m) = 1, are considered. The cardinalities of the sets of minimal codewords of weights 10 and 11 in codes C and of weight 12 in their extended codes ^C are determined. The weight distributions of minimal codewords in the binary Reed-Mullercodes RM (3, 6) and RM (3, 7) are determined. The applied method enablescodes with larger parameters to be attacked.<br/><br/>Description: 2000 Mathematics Subject Classification: 94B05, 94B15.Cohomology of the G-Hilbert Scheme for 1/r(1,1,R−1)
http://hdl.handle.net/10525/1740
Title: Cohomology of the G-Hilbert Scheme for 1/r(1,1,R−1)<br/><br/>Authors: Kędzierski, Oskar<br/><br/>Abstract: In this note we attempt to generalize a few statements drawn from the 3-dimensional McKay correspondence to the case of a cyclic groupnot in SL(3, C). We construct a smooth, discrepant resolution of the cyclic, terminal quotient singularity of type 1/r(1,1,r−1), which turns out to be isomorphic to Nakamura’s G-Hilbert scheme. Moreover we explicitly describe tautological bundles and use them to construct a dual basis to the integral cohomology on the resolution.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 14E15; Secondary 14C05,14L30.A Smooth Four-Dimensional G-Hilbert Scheme
http://hdl.handle.net/10525/1739
Title: A Smooth Four-Dimensional G-Hilbert Scheme<br/><br/>Authors: Sebestean, Magda<br/><br/>Abstract: When the cyclic group G of order 15 acts with some specific weights on affine four-dimensional space, the G-Hilbert scheme is a crepantresolution of the quotient A^4 / G. We give an explicit description of this resolution using G-graphs.<br/><br/>Description: 2000 Mathematics Subject Classification: 14C05, 14L30, 14E15, 14J35.Involution Matrix Algebras – Identities and Growth
http://hdl.handle.net/10525/1738
Title: Involution Matrix Algebras – Identities and Growth<br/><br/>Authors: Rashkova, Tsetska<br/><br/>Abstract: The paper is a survey on involutions (anti-automorphisms of order two) of different kinds. Starting with the first systematic investigationson involutions of central simple algebras due to Albert the author emphasizes on their basic properties, the conditions on their existence and their correspondence with structural characteristics of the algebras.Focusing on matrix algebras a complete description of involutions of thefirst kind on Mn(F) is given. The full correspondence between an involution of any kind for an arbitrary central simple algebra A over a field F of characteristic 0 and an involution on Mn(A) specially defined is studied.The research mainly in the last 40 years concerning the basic properties ofinvolutions applied to identities for matrix algebras is reviewed starting withthe works of Amitsur, Rowen and including the newest results on the topic.The cocharactes, codimensions and growth of algebras with involutions areconsidered as well.<br/><br/>Description: 2000 Mathematics Subject Classification: 16R50, 16R10.Complex Hyperbolic Surfaces of Abelian Type
http://hdl.handle.net/10525/1737
Title: Complex Hyperbolic Surfaces of Abelian Type<br/><br/>Authors: Holzapfel, R.<br/><br/>Abstract: We call a complex (quasiprojective) surface of hyperbolic type,iff – after removing finitely many points and/or curves – the universal coveris the complex two-dimensional unit ball. We characterize abelian surfaceswhich have a birational transform of hyperbolic type by the existence of areduced divisor with only elliptic curve components and maximal singularityrate (equal to 4). We discover a Picard modular surface of Gauß numbersof bielliptic type connected with the rational cuboid problem. This paper isalso necessary to understand new constructions of Picard modular forms of3-divisible weights by special abelian theta functions.<br/><br/>Description: 2000 Mathematics Subject Classification: 11G15, 11G18, 14H52, 14J25, 32L07.Equimultiple Locus of Embedded Algebroid Surfaces and Blowing–up in Characteristic Zero
http://hdl.handle.net/10525/1736
Title: Equimultiple Locus of Embedded Algebroid Surfaces and Blowing–up in Characteristic Zero<br/><br/>Authors: Piedra-Sánchez, R.; Tornero, J.<br/><br/>Abstract: The smooth equimultiple locus of embedded algebroid surfacesappears naturally in many resolution processes, both classical and modern.In this paper we explore how it changes by blowing–up.<br/><br/>Description: 2000 Mathematics Subject Classification: 14B05, 32S25.Dickson Polynomials that are Permutations
http://hdl.handle.net/10525/1735
Title: Dickson Polynomials that are Permutations<br/><br/>Authors: Cipu, Mihai<br/><br/>Abstract: A theorem of S.D. Cohen gives a characterization for Dicksonpolynomials of the second kind that permutes the elements of a finite fieldof cardinality the square of the characteristic. Here, a different proof ispresented for this result.<br/><br/>Description: 2000 Mathematics Subject Classification: 11T06, 13P10.On the Factorization of the Poincaré Polynomial: A Survey
http://hdl.handle.net/10525/1734
Title: On the Factorization of the Poincaré Polynomial: A Survey<br/><br/>Authors: Akyıldız, Ersan<br/><br/>Abstract: Factorization is an important and very difficult problem in mathematics. Finding prime factors of a given positive integer n, or findingthe roots of the polynomials in the complex plane are some of the important problems not only in algorithmic mathematics but also in cryptography.<br/><br/>Description: 2000 Mathematics Subject Classification: 13P05, 14M15, 14M17, 14L30.Automorphisms of the Planar Tree Power Series Algebra and the Non-Associative Logarithm
http://hdl.handle.net/10525/1733
Title: Automorphisms of the Planar Tree Power Series Algebra and the Non-Associative Logarithm<br/><br/>Authors: Gerritzen, L.<br/><br/>Abstract: In this note we present the formula for the coefficients of the substitution series f(g(x)) of planar tree power series g(x) into f(x).<br/><br/>Description: 2000 Mathematics Subject Classification: 17A50, 05C05.Z2-Graded Polynomial Identities for Superalgebras of Block-Triangular Matrices
http://hdl.handle.net/10525/1732
Title: Z2-Graded Polynomial Identities for Superalgebras of Block-Triangular Matrices<br/><br/>Authors: Di Vincenzo, Onofrio<br/><br/>Abstract: We present some results about the Z2-graded polynomial identities of block-triangular matrix superalgebras R[[A M],[0 B]]. In particular, we describe conditions for the T2-ideal of a such superalgebra to be factorable as the product T2(A)T2(B). Moreover, we give formulas for computing the sequence of the graded cocharacters of R in some interesting case.<br/><br/>Description: 000 Mathematics Subject Classification: Primary 16R50, Secondary 16W55.