Related papers: Normal subgroups and support $\tau$-tilting module…

Suppose that $\tilde{G}$ is a connected reductive group defined over a field $k$, and $\Gamma$ is a finite group acting via $k$-automorphisms of $\tilde{G}$ satisfying a certain quasi-semisimplicity condition. Then the connected part of the…

Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring and $M$ a graded $R$-module. In this paper, we introduce the concept of graded primary-like submodules as a new generalization of graded primary ideals and give…

For a finite dimensional algebra $\Lambda$ and a non-negative integer $n$, we characterize when the set $\tilt_n\Lambda$ of additive equivalence classes of tilting modules with projective dimension at most $n$ has a minimal (or…

In this paper we consider the Fitting subgroup $F(G)$ of a finite group $G$ and its generalizations: the quasinilpotent radical $F^*(G)$ and the generalized Fitting subgroup $\tilde{F}(G)$ defined by $\tilde{F}(G)\supseteq \Phi(G)$ and…

We investigate the representation theory of domestic group schemes $\mathcal{G}$ over an algebraically closed field of characteristic $p > 2$. We present results about filtrations of induced modules, actions on support varieties, Clifford…

In the case of complex symplectic and orthogonal groups, we find $(\mathfrak{g}, K)-$modules with the property that their $K-$structure matches the structure of regular functions on the closures of nilpotent orbits. This establishes a…

Let $c:\mathcal{G}\to\R$ be a cocycle on a locally compact Hausdorff groupoid $\mathcal{G}$ with Haar system. Under some mild conditions (satisfied by all integer valued cocycles on \'{e}tale groupoids), $c$ gives rise to an unbounded odd…

Let k be the field with p>0 elements, and let G be a finite group. By exhibiting an E-infinity-operad action on Hom(P,k) for a complete projective resolution P of the trivial kG-module k, we obtain power operations of Dyer-Lashof type on…

For a real reductive linear Lie group G, the space of Whittaker functions is the representation space induced from a non-degenerate unitary character of the Iwasawa nilpotent subgroup. Defined are the standard Whittaker (g,K)-modules, which…

In this article we prove that the numerical Grothendieck group of every smooth proper dg category is invariant under primary field extensions, and also that the mod-n algebraic K-theory of every dg category is invariant under extensions of…

Let $G$ be a simple and simply connected algebraic group over an algebraically closed field $\Bbbk$ of characteristic $p>0$. We establish an isomorphism of $G$-modules between a direct sum of modules $\text{St} \otimes \text{St}$ and a…

Let $R$ be an algebra over a ring $\Bbbk$, $T$ an $R$-algebra, $M$ a finitely generated projective $R$-module, and $N$ a $T$-module. Let $G$ be a linearly reductive group scheme over $\Bbbk$ equipped with a representation…

It is demonstrated that any almost-tilting module over a gentle algebra is indeed partial-tilting, meaning it can be completed as a tilting module. Furthermore, such a module has at most $2n$ possible complements, thereby confirming a…

We investigate the homology of finite index subgroups G_i of a given finitely presented group G. Specifically, we examine d_p(G_i), which is the dimension of the first homology of G_i, with mod p coefficients. We say that a collection of…

In this paper, we show that for an algebra $\Lambda$ with radical square zero and an indecomposable $\Lambda$-module $M$ such that $\Lambda$ is Gorenstein of finite type or $\tau M$ is $\tau$-rigid, $M$ is $\tau$-rigid if and only if the…

Let V be a vertex operator algebra, and for k a positive integer, let g be a k-cycle permutation of the vertex operator algebra V^{\otimes k}. We prove that the categories of weak, weak admissible and ordinary g-twisted modules for the…

In this paper we study a natural decomposition of $G$-equivariant $K$-theory of a proper $G$-space, when $G$ is a Lie group with a compact normal subgroup $A$ acting trivially. Our decomposition could be understood as a generalization of…

Let G be a Lie group with Lie algebra $\mathfrak{g}$, $h \in \frak{g}$ an element for which the derivation ad(h) defines a 3-grading of $\mathfrak{g}$ and $\tau_G$ an involutive automorphism of G inducing on $\mathfrak{g}$ the involution…

Let $(R, \mf, k_R)$ be regular local $k$-algebra satisfying the weak Jacobian criterion, such that $k_R/k$ is an algebraic field extension. Let $D_R$ be the ring of $k$-linear differential operators of $R$. We give an explicit decomposition…

Let $mathfrak{g}$ be a restricted Lie superalgebra over an algebraically closed field $k$ of characteristic $p>2$. Let $\mathfrak{u}(\mathfrak{g})$ denote the restricted enveloping algebra of $\mathfrak{g}$. In this paper we prove that the…