Gradings and Symmetries on Heisenberg type 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.

References in corpus (6)

• Gradings on the Albert Algebra and on $f_4$
• Classification of group gradings on simple Lie algebras of types A, B, C and D
• Group Gradings on Simple Lie Algebras of Type "A"
• Generalized Heisenberg algebra coherent states for Power-law potentials
• Automorphisms of the fine grading of sl(n,C) associated with the generalized Pauli matrices
• Group gradings on filiform Lie algebras