Related papers: Bongartz ${\tau}$-Complements Over Split-By-Nilpot…

Let $A$ be a coherent algebra and $B$ be a finite-dimensional Gorenstein algebra over a field $k$. We describe finitely presented Gorenstein projective $A\otimes_k B$-modules in terms of their underlying onesided modules. Moreover, if the…

In this note we compare the a-invariant of a homogeneous algebra B to the a-invariant of a subalgebra A. In particular we show that if $A \subset B$ is a finite homogeneous inclusion of standard graded domains over an algebraically closed…

Let $\mu$ denot the infinite convolution generated by $\{(N_k,B_k)\}_{k=1}^\infty$ given by $$ \mu =\delta_{{N_1}^{-1}B_1}\ast\delta_{(N_1N_2)^{-1}B_2}\ast\dots\ast\delta_{(N_1N_2\cdots N_k)^{-1}B_k} *\cdots. $$ where $B_k$ is a complete…

Support $\tau$-tilting modules correspond to some classes of categorical objects bijectively, such as two-term tilting complexes for any finite dimensional symmetric algebra. This fact motivates us to classify support $\tau$-tilting modules…

In this paper, we study the representation theory of the universal central extension $\mathcal{G}$ of the infinite-dimensional Galilean conformal algebra, introduced by Bagchi-Gopakumar, in $(2+1)$ dimensional space-time, which was named…

We prove that (a) the sections space of a continuous unital subhomogeneous $C^*$ bundle over compact metrizable $X$ admits a finite-index expectation onto $C(X)$, answering a question of Blanchard-Gogi\'{c} (in the metrizable case); (b)…

We present modules for the extended affine Lie algebra $\widetilde{\frak{gl}_{3}(\bc_q)}$ by using the idea of free fields. A necessary and sufficient condition for the modules being unitary is given.

Given a finite root system $\Phi$, we show that there is an integer $c=c(\Phi)$ such that $\dim\Ext_G^1(L,L')<c$, for any reductive algebraic group $G$ with root system $\Phi$ and any irreducible rational $G$-modules $L,L'$. There also is…

Quantum Chern-Simons invariants of differentiable manifolds are analyzed from the point of view of homological algebra. Given a manifold M and a Lie (or, more generally, an L-infinity) algebra g, the vector space H^*(M) \otimes g has the…

We show that the unit ball of a full Hilbert $C^*$-module is sequentially compact in a certain weak topology if and only if the underlying $C^*$-algebra is finite dimensional. This provides an answer to the question posed in J.…

We prove a Gauss-Bonnet theorem for (finite coverings of) moduli spaces of Riemann surfaces endowed with the McMullen metric. The proof uses properties of an exhaustion of moduli spaces by compact submanifolds with corners and the…

We provide new criteria for the integrality and birationality of an extension of graded algebras in terms of the general notion of polar multiplicities of Kleiman and Thorup. As an application, we obtain a new criterion for when a module is…

We consider the Springer fiber ${\mathcal B}_u$ corresponding to a nilpotent endomorphism $u$ of nilpotent order 2. As a first result, we give a description of the elements of a given component of ${\mathcal B}_u$ which are fixed by the…

A finite algebra $\bA=\alg{A;\cF}$ is \emph{dualizable} if there exists a discrete topological relational structure $\BA=\alg{A;\cG;\cT}$, compatible with $\cF$, such that the canonical evaluation map $e\_{\bB}\colon \bB\to \Hom(…

Let $G$ be a connected and simply connected two-step nilpotent Lie group and $\Gamma$ a lattice subgroup of $G$. In this note, we give a new multiplicity formula, according to the sense of Moore, of irreducible unitary representations…

First, we study recollement of a derived category of unbounded complexes of modules induced by a partial tilting complex. Second, we give equivalent conditions for P^{centerdot} to be a recollement tilting complex, that is, a tilting…

Algebra extensions A < B where A is a left B-module such that the B-action extends the multiplication in A are ubiquitous. We encounter examples of such extensions in the study of group actions, group gradings or more general Hopf actions…

Necessary and sufficient conditions are given for a $G$-graded simple module over a unital associative algebra, graded by an abelian group $G$, to be isomorphic to a loop module of a simple module, as well as for two such loop modules to be…

We study a version of the BGG category O for Dynkin Borel subalgebras of root-reductive Lie algebras g, such as gl(\infty). We prove results about extension fullness and compute the higher extensions of simple modules by Verma modules. In…

We prove a variant of the so-called bilinear embedding theorem for operators in divergence form with complex coefficients and with nonnegative locally integrable potentials, subject to mixed boundary conditions, and acting on arbitrary open…