Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHarish-Chandra modules over invariant subalgebras in a skew-group ring
208
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We construct a new class of algebras resembling enveloping algebras and generalizing orthogonal Gelfand-Zeitlin algebras and rational Galois algebras studied by [EMV,FuZ,RZ,Har]. The algebras are defined via a geometric realization in terms of sheaves of functions invariant under an action of a finite group. A natural class of modules over these algebra can be constructed via a similar geometric realization. In the special case of a local reflection group, these modules are shown to have an explicit basis, generalizing similar results for orthogonal Gelfand-Zeitlin algebras from [EMV] and for rational Galois algebras from [FuZ]. We also construct a family of canonical simple Harish-Chandra modules and give sufficient conditions for simplicity of some modules.
rate research
Read More
In this paper, we classify all indecomposable Harish-Chandra modules of the intermediate series over the twisted Heisenberg-Virasoro algebra. Meanwhile, some bosonic modules are also studied.
We use analogues of Enrights and Arkhipovs functors to determine the quiver and relations for a category of $mathfrak{sl}_2 ltimes L(4)$-modules which are locally finite (and with finite multiplicities) over $mathfrak{sl}_2$. We also outline serious obstacles to extend our result to $mathfrak{sl}_2 ltimes L(k)$, for $k>4$.
Mathematical physicists have studied degenerations of Lie groups and their representations, which they call contractions. In this paper we study these contractions, and also other families, within the framework of algebraic families of Harish-Chandra modules. We construct a family that incorporates both a real reductive group and its compact form, separate parts of which have been studied individually as contractions. We give a complete classification of generically irreducible families of Harish-Chandra modules in the case of the family associated to SL(2, R).
We give conditions for unitarizability of Harish-Chandra super modules for Lie supergroups and superalgebras.
We partially generalize Peters formula on modules over the group ring ${mathbb F} Gamma$ for a given finite field ${mathbb F}$ and a sofic group $Gamma$. It is also discussed that how the values of entropy are related to the zero divisor conjecture.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
