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Munayim Dilxat

Publications and source records attributed to Munayim Dilxat.

4 recordsLinked to original sources
arXiv2022

$U(\frak h)$-free modules over the Lie algebras of differential operators

In this paper, we consider some non-weight modules over the Lie algebra of Weyl type. First, we determine the modules whose restriction to $U(\frak h)$ are free of rank $1$ over the Lie algebra of differential operators on the circle. Then we determine the necessary and sufficient conditions for the tensor products of quasi-finite highest weight modules and $U(\frak h)$-free modules to be irreducible, and obtain that any two such tensor products are isomorphic if and only if the corresponding highest weight modules and $U(\frak h)$-free modules are isomorphic. Finally, we extend such results to the Lie algebras of differential operators in the general case.

math.RT↗
arXiv2022

Classification of simple Harish-Chandra modules over the Ovsienko-Roger superalgebra

With the $Ω$-operators for the Virasoro algebra \cite{BF} and the super Virasoro algebra in \cite{CL, CLL}, we get the $Ω$-operators for the Ovsienko-Roger superalgebras in this paper and then use it to classify all simple cuspidal modules for the $\bZ$-graded and $\frac12\bZ$-graded Ovsienko-Roger superalgebras. By this result, we can easily classify all simple Harish-Chandra modules over some related Lie superalgebras, including the $N=1$ BMS$_3$ algebra, the super $W(2,2)$, etc.

math.RT↗