Gradings and Symmetries on Heisenberg type algebras
A. Calder\'on, C. Draper, C. Mart\'in, T. S\'anchez
TL;DR
This paper classifies fine group gradings on various Heisenberg algebras and superalgebras, computes their Weyl groups, and applies these results to Heisenberg Lie color algebras, advancing understanding of their symmetry structures.
Contribution
It provides a comprehensive description of gradings and Weyl groups on Heisenberg and superalgebras, including new applications to Lie color algebras.
Findings
Classification of fine gradings on Heisenberg algebras and superalgebras
Computation of Weyl groups for these gradings
Application to Heisenberg Lie color algebras
Abstract
We describe the fine (group) gradings on the Heisenberg algebras, on the Heisenberg superalgebras and on the twisted Heisenberg algebras. We compute the Weyl groups of these gradings. Also the results obtained respect to Heisenberg superalgebras are applied to the study of Heisenberg Lie color algebras.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Matrix Theory and Algorithms