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arXiv · 1701.06844

Pauli gradings on Lie superalgebras and graded codimension growth

Dušan D. Repovš·Mikhail V. Zaicev
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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 polyomial identities of Lie superalgebras. In particular, we compute graded PI-exponent corresponding to Pauli grading.

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Dušan D. Repovš, Mikhail V. Zaicev. 2017-01-24. Pauli gradings on Lie superalgebras and graded codimension growth. https://doi.org/10.1016/j.laa.2017.01.023

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