相关论文: Killing of supports on graded algebras

This dissertation concerns the classification of groupoid and higher-rank graph C*-algebras and has two main components. Firstly, for a groupoid it is shown that the notions of strength of convergence in the orbit space and…

The space of de Rham currents supported in finitely many points in a Lie group $G$ has the structure of a filtered differential graded Hopf algebra. The product is given by convolution of compactly supported currents, and the co-product…

We introduce the notion of the $\infty$-category of (complete) derived $G$-graded modules over a $G$-graded ring $R$ for a torsion-free abelian group $G$, and we study its foundational properties. Moreover, we prove a categorical…

Let $H$ be a numerical semigroup. We give effective bounds for the multiplicity $e(H)$ when the associated graded ring $\operatorname{gr}_\mathfrak{m} K[H]$ is defined by quadrics. We classify Koszul complete intersection semigroups in…

Let i be a homomorphism of the multiplicative group into a connected reductive algebraic group over C. Let G^i be the centralizer of the image i. Let LG be the Lie algebra of G and let L_nG (n integer) be the summands in the direct sum…

We investigate a question posed by Gaberdiel and Gannon concerning the relationship between $C_{2}$-algebras and twisted modules. To each twisted module $W$ of a vertex algebra $V$, we first associate a decreasing sequence of subspaces…

Let $A = \bigoplus_{i \geqslant 0} A_i$ be a graded locally finite $k$-algebra such that $A_0$ is an arbitrary finite-dimensional algebra satisfying some splitting condition. In this paper we develop a generalized Koszul theory generalizing…

We obtain Koszul-type dualities for categories of graded modules over a graded associative algebra which can be realized as the semidirect product of a bialgebra coinciding with its degree zero part and a graded module algebra for the…

Motivated by $\tau$-tilting theory developed by Adachi, Iyama and Reiten, for a finite-dimensional algebra $\Lambda$ with action by a finite group $G$, we introduce the notion of $G$-stable support $\tau$-tilting modules. Then we establish…

A theory of graded manifolds can be viewed as a generalization of differential geometry of smooth manifolds. It allows one to work with functions which locally depend not only on ordinary real variables, but also on $\mathbb{Z}$-graded…

Let A,B be finite dimensional G-graded algebras over an algebraically closed field K with char(K)=0, where G is an abelian group, and let Id_G(A) be the set of graded identities of A (res. Id_G(B)). We show that if A,B are G-simple then…

Given a reductive algebraic group $G$ and a finite dimensional algebraic $G$-module $V$, we study how close is the algebra of $G$-invariant polynomials on $V^{\oplus n}$ to the subalgebra generated by polarizations of $G$-invariant…

In this article, we introduce the concepts of graded $s$-prime submodules which is a generalization of graded prime submodules. We study the behavior of this notion with respect to graded homomorphisms, localization of graded modules,…

We establish a connection between two areas of independent interest in representation theory, namely Koszul duality and higher homological algebra. This is done through a generalization of the notion of $T$-Koszul algebras, for which we…

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…

We settle a long-standing problem in the theory of Hecke algebras of complex reflection groups by constructing many (graded) integral cellular bases of these algebras. As applications, we explicitly construct the simple modules of Ariki's…

This paper continues the study of cluster algebras initiated in math.RT/0104151. Its main result is the complete classification of the cluster algebras of finite type, i.e., those with finitely many clusters. This classification turns out…

Let A and B be finite dimensional simple real algebras with division gradings by an abelian group G. In this paper we give necessary and sufficient conditions for the coincidence of the graded identities of A and B. We also prove that every…

We investigate notions of support and cosupport for differential graded (DG) modules over DG algebras. We apply these notions to identify certain classes of derived functors that are able to detect triviality and isomorphisms in derived…

We show that the graded maximal ideal of a graded $K$-algebra $R$ has linear quotients for a suitable choice and order of its generators if the defining ideal of $R$ has a quadratic Gr\"obner basis with respect to the reverse lexicographic…