BulDML at Institute of Mathematics and Informatics >
IMI Periodicals >
Serdica Mathematical Journal >
2008 >
Volume 34, Number 2 >

Please use this identifier to cite or link to this item:

Title: q-Leibniz Algebras
Authors: Dzhumadil'daev, A. S.
Keywords: Leibniz Algebras
Zinbiel Algebras
Omni-Lie Algebras
Polynomial Identities
Issue Date: 2008
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 34, No 2, (2008), 415p-440p
Abstract: An algebra (A,ο) is called Leibniz if aο(bοc) = (a ο b)ο c-(a ο c) ο b for all a,b,c ∈ A. We study identities for the algebras A(q) = (A,οq), where a οq b = a ο b+q b ο a is the q-commutator. Let Char K ≠ 2,3. We show that the class of q-Leibniz algebras is defined by one identity of degree 3 if q2 ≠ 1, q ≠−2, by two identities of degree 3 if q = −2, and by the commutativity identity and one identity of degree 4 if q = 1. In the case of q = −1 we construct two identities of degree 5 that form a base of identities of degree 5 for −1-Leibniz algebras. Any identity of degree < 5 for −1-Leibniz algebras follows from the anti-commutativity identity.
Description: 2000 Mathematics Subject Classification: Primary 17A32, Secondary 17D25.
ISSN: 1310-6600
Appears in Collections:Volume 34, Number 2

Files in This Item:

File Description SizeFormat
2008-415-440.pdf490.82 kBAdobe PDFView/Open


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.


Valid XHTML 1.0!   Creative Commons License