Pauli gradings on Lie superalgebras and graded codimension growth

Repovš, Dušan (author), Zaicev, Mikhail V. (author)

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.

• Language: English
• Keywords: polynomial identities, Lie superalgebras, graded algebras, codimensions, exponential growth, Pauli gradings
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2017
• Number of pages: Str. 134-150
• Numbering: Vol. 520
• PID: 20.500.12556/RUL-110335
• UDC: 512.554
• ISSN on article: 0024-3795
• DOI: http://dx.doi.org/10.1016/j.laa.2017.01.023
• COBISS.SI-ID: 17887321
• Publication date in RUL: 13.09.2019

Record is a part of a journal

• Title: Linear algebra and its applications
• Shortened title: Linear algebra appl.
• Publisher: North Holland
• ISSN: 0024-3795
• COBISS.SI-ID: 1119247