Pauli gradings on Lie superalgebras and graded codimension growth

Dušan Repovš (Author), Mikhail Zaicev (Author)

Abstract

We introduce grading on certain finite dimensional simple Lie superalgebras of type ▫$P(t)$▫ by elementary abelian 2-group. This grading gives rise to Pauli matrices and is a far generalization of ▫$(\mathbb{Z}_2 \times \mathbb{Z}_2)$▫-grading on Lie algebra of ▫$(2 \times 2)$▫-traceless matrices.We use this grading for studying numerical invariants of polynomial identities of Lie superalgebras. In particular, we compute graded PI-exponent corresponding to Pauli grading.

Keywords

polynomial identities;Lie superalgebras;graded algebras;codimensions;exponential growth;Pauli gradings;

Data

Language:	English
Year of publishing:	2017
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	512.554
COBISS:	17887321
ISSN:	0024-3795
Views:	567
Downloads:	274
Average score:	0 (0 votes)
Metadata:

Other data

Type (COBISS):	Article
Pages:	str. 134-150
Issue:	ǂVol. ǂ520
Chronology:	2017
DOI:	http://dx.doi.org/10.1016/j.laa.2017.01.023
ID:	11222886