相关论文: Representations of the Grassmann Poisson superalge…

Let $A$ be a Poisson Hopf algebra over an algebraically closed field of characteristic zero. If $A$ is finitely generated and connected graded as an algebra and its Poisson bracket is homogeneous of degree $d \geq 0$, then $A$ is…

We point out, and draw some consequences of, the fact that the Poisson Lie group G* dual to G=GL_n(C) (with its standard complex Poisson structure) may be identified with a certain moduli space of meromorphic connections on the unit disc…

We give the algebraic and geometric classification of complex four-dimensional Jordan superalgebras. In particular, we describe all irreducible components in the corresponding varieties.

Let G be an almost simple, simply connected algebraic group over an algebraically closed field of characteristic p>0. In this paper we restate our conjecture from 1979 on the characters of irreducible modular representations of G so that it…

We introduce the quasi-Poisson enveloping algebra and Poisson enveloping algebra for a non-commutative Poisson algebra. We prove that for a non-commutative Poisson algebra, the category of quasi-Poisson modules is equivalent to the category…

It is shown that every $2$-shifted Poisson structure on a finitely generated semi-free commutative differential graded algebra $A$ defines a very explicit infinitesimal $2$-braiding on the homotopy $2$-category of the symmetric monoidal…

Dave Benson conjectured in 2020 that if $G$ is a finite $2$-group and $V$ is an odd-dimensional indecomposable representation of $G$ over an algebraically closed field $\Bbbk$ of characteristic $2$, then the only odd-dimensional…

Each $\frac{1}{2}$-derivation of the planar Galilean conformal algebra is proven to be a scalar. As a corollary, all transposed Poisson structures on the planar Galilean conformal algebra are trivial.

The irreducible components of varieties parametrizing the finite dimensional representations of a finite dimensional algebra $\Lambda$ are explored, with regard to both their geometry and the structure of the modules they encode. Provided…

Let $G$ be a complex reductive connected algebraic group equipped with the Sklyanin bracket. A classification of Poisson homogeneous $G$-spaces with connected isotropy subgroups is given. This result is based on Drinfeld's correspondence…

Let $p$ be a prime number and $\Bbbk=\bar{\mathbb{F}}_p$, the algebraic closure of the finite field $\mathbb{F}_p$ of $p$ elements. Let ${\bf G}$ be a connected reductive group defined over $\mathbb{F}_p$ and ${\bf B}$ be a Borel subgroup…

Let $k$ be an arbitrary field of characteristic $0$. It is shown that for any $n\geq 1$ the universal enveloping algebras of the Poisson symplectic algebra $P_n(k)$ and the Weyl algebra $A_n(k)$ are isomorphic and the canonical isomorphism…

We study Poisson varieties $(\mathrm{SL}_n,\pi_{\bar{\mathbf{\Gamma}}}^{\dagger})$ parameterized by Belavin--Drinfeld quadruples $\bar{\mathbf{\Gamma}}:=(\mathbf{\Gamma},r_0)$ of type $A_{n-1}$ along with generalized cluster structures…

Let $G$ be a semisimple Lie group. We describe the irreducible representations of $G$ by linear isometries on $L_p$-spaces for $p\in (1,+\infty)$ with $p\neq 2.$ More precisely, we show that, for every such representation $\pi,$ there…

In this article, we investigate the representations of the Drinfeld doubles $D(R_{mn}(q))$ of the Radford Hopf algebras $R_{mn}(q)$ over an algebraically closed field $\Bbbk$, where $m>1$ and $n>1$ are integers and $q\in\Bbbk$ is a root of…

We determine the graded composition multiplicity in the symmetric algebra S(V) of the natural GL_n(q)-module V, or equivalently in the coinvariant algebra of V, for a large class of irreducible modules around the Steinberg module. This was…

We construct quadratic finite-dimensional Poisson algebras and their quantum versions related to rank N and degree one vector bundles over elliptic curves with n marked points. The algebras are parameterized by the moduli of curves. For N=2…

We classify all conformal irreducible modules of finite type over the Cheng Kac superalgebra CK(6).

A celebrated theorem by Gelfand-Kazhdan states that the restriction of any cuspidal irreducible representations of $GL_n(\mathcal{K})$ over local field to the mirabolic subgroup $P$ is isomorphic to the standard irreducible representation…

Playing off against each other the real and complex structures, we elucidate the local structure of certain representation spaces in the world of Poisson geometry. Particular cases of these spaces arise as moduli spaces of semistable…