Related papers: On tilting complexes over blocks covering cyclic b…

We study the properties of tilting modules in the context of properly stratified algebras. In particular, we answer the question when the Ringel dual of a properly stratified algebra is properly stratified itself, and show that the class of…

We compute rationally the topological (complex) K-theory of the classifying space BG of a discrete group provided that G has a cocompact G-CW-model for its classifying space for proper G-actions. For instance word-hyperbolic groups and…

Non-singular weighted surface algebras satisfy the necessary condition found in [6] for existence of cluster tilting modules. We show that any such algebra whose Gabriel quiver is bipartite, has a module satisfying the necessary ext…

Let $D$ be a non-commutative division ring, $G$ a subnormal subgroup of ${\mathrm GL}_n(D)$. In this note we show that if $G$ contains a non-abelian solvable maximal subgroup, then $n=1$ and $D$ is a cyclic algebra of prime degree over $F$.

Suppose that all nontrivial subsections of a $p$-block $B$ are conjugate (where $p$ is a prime). By using the classification of the finite simple groups, we prove that the defect groups of $B$ are either extraspecial of order $p^3$ with $p…

We investigate deformations of skew group algebras that arise from a finite cyclic group acting on a polynomial ring in positive characteristic, where characteristic divides the order of the group. We allow deformations which deform both…

Let G be a finite group. The Plesken Lie algebra L[G] is a subalgebra of the complex group algebra C[G] and admits a direct-sum decomposition into simple Lie algebras based on the ordinary character theory of G. In this paper we review the…

Let $G$ be a finite group, and let $\Delta(G)$ be the prime graph built on its set of conjugacy class sizes: this is the (simple undirected) graph whose vertices are the prime numbers dividing some conjugacy class size of $G$, and two…

We show how a cluster-tilted algebra of finite representation type is related to the corresponding tilted algebra, in the case of algebras defined over an algebraically closed field.

We show that an algebraic 2-Calabi-Yau triangulated category over an algebraically closed field is a cluster category if it contains a cluster tilting subcategory whose quiver has no oriented cycles. We prove a similar characterization for…

Let $A$ be a finite dimensional hereditary algebra over a field $k$ and $A^{(1)}$ the duplicated algebra of $A$. We first show that the global dimension of endomorphism ring of tilting modules of $A^{(1)}$ is at most 3. Then we investigate…

Let $G$ be a finite group of odd order, $\F$ a finite field of odd characteristic $p$ and $\B$ a finite--dimensional symplectic $\F G$-module. We show that $\B$ is $\F G$-hyperbolic, i.e., it contains a self--perpendicular $\F G$-submodule,…

Let k be an algebraically closed field of positive characteristic p. We consider which finite groups G have the property that every faithful action of G on a connected smooth projective curve over k lifts to characteristic zero. Oort…

In this paper, we classify the modular group algebra $KG$ of a group $G$ over a field $K$ of characteristic $p>0$ having upper Lie nilpotency index $t^{L}(KG)= \vert G^{\prime}\vert - k(p-1) + 1$ for $k=14$ and $15$. Group algebras of upper…

Suppose $\ell$ is a prime number, $\ell >3$, $K$ is a field that is an unramified finite extension of the field $\Q_\ell$ of $\ell$-adic numbers, and $G$ is a finite group that is a semi-direct product of a normal $\ell'$-subgroup $H$ and a…

Let $G$ be a finite group and construct a graph $\Delta(G)$ by taking $G\setminus\{1\}$ as the vertex set of $\Delta(G)$ and by drawing an edge between two vertices $x$ and $y$ if $\langle x,y\rangle$ is cyclic. Let $K(G)$ be the set…

In this paper, we compute the number of two-term tilting complexes for an arbitrary symmetric algebra with radical cube zero over an algebraically closed field. Firstly, we give a complete list of symmetric algebras with radical cube zero…

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…

This paper describes the $K$-theory structure for three algebra classes. For cyclic $p$-group rings and truncated polynomial rings over $\mathbb{Z}/p^s\mathbb{Z}$, we determine reduced $K_2$-structures via a common algebraic framework. For…

Let $p$ be a prime. In this paper, we compute complexities of some simple modules of symmetric groups labelled by two-part partitions. Most of the simple modules considered here are contained in the $p$-blocks with non-abelian defect…