Displaying similar documents to “Relationships between generalized Heisenberg algebras and the classical Heisenberg algebra”

Generalised Jantzen filtration of Lie superalgebras I

Yucai Su, R. B. Zhang (2012)

Journal of the European Mathematical Society

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A Jantzen type filtration for generalised Verma modules of Lie superalgebras is introduced. In the case of type I Lie superalgebras, it is shown that the generalised Jantzen filtration for any Kac module is the unique Loewy filtration, and the decomposition numbers of the layers of the filtration are determined by the coefficients of inverse Kazhdan–Lusztig polynomials. Furthermore, the length of the Jantzen filtration for any Kac module is determined explicitly in terms of the degree...

Braided modules and reflection equations

Dimitri Gurevich (1997)

Banach Center Publications

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We introduce a representation theory of q-Lie algebras defined earlier in [DG1], [DG2], formulated in terms of braided modules. We also discuss other ways to define Lie algebra-like objects related to quantum groups, in particular, those based on the so-called reflection equations. We also investigate the truncated tensor product of braided modules.

Cohomology and deformations of 3-dimensional Heisenberg Hom-Lie superalgebras

Junxia Zhu, Liangyun Chen (2021)

Czechoslovak Mathematical Journal

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We study Hom-Lie superalgebras of Heisenberg type. For 3-dimensional Heisenberg Hom-Lie superalgebras we describe their Hom-Lie super structures, compute the cohomology spaces and characterize their infinitesimal deformations.