Related papers: Relative left Bongartz completions and their compa…

Let $G$ be a finite group of Lie type and $T$ a maximal torus of $G$. In this paper we complete the study of the question of the existence of a complement for the torus $T$ in its algebraic normalizer $N(G,T)$. It is proved that every…

We show that it is in principle possible to construct dualities between commutative and non-commutative theories in a systematic way. This construction exploits a generalization of the exact renormalization group equation (ERG). We apply…

We obtain a characterization of left perfect rings via superstability of the class of flat left modules with pure embeddings. $\mathbf{Theorem.}$ For a ring $R$ the following are equivalent. - $R$ is left perfect. - The class of flat left…

We investigate purities determined by classes of finitely presented modules including the correspondence between purities for left and right modules. We show some cases where purities determined by matrices of given sizes are different.…

We obtain a series of new results on the problem of irreducibility of commuting varieties associated with symmetric pairs or, in other words, $Z_2$-graded simple Lie algebras. In particular, we present many examples of reducible commuting…

APR tilts for path algebra $kQ$ can be realized as the mutation of the quiver $Q$ in $\mathbb Z Q$ with respect to the translation. In this paper, we show that we have similar results for the quadratic dual of truncations of $n$-translation…

We apply the super duality formalism recently developed by the authors to obtain new equivalences of various module categories of general linear Lie superalgebras. We establish the correspondence of standard, tilting, and simple modules, as…

We prove relative versions of many earlier results about almost invariant sets and splittings of groups. In particular, we prove a relative version of the algebraic torus theorem, and we prove the existence and uniqueness of relative…

We prove the Landau-Ginzburg Mirror Symmetry Conjecture at the level of (orbifolded) Frobenius algebras for a large class of invertible singularities, including arbitrary sums of loops and Fermats with arbitrary symmetry groups.…

Let G be a reductive p-adic group and let H(G)^s be a Bernstein block of the Hecke algebra of G. We consider two important topological completions of H(G)^s: a direct summand S(G)^s of the Harish-Chandra--Schwartz algebra of G and a…

For finite-dimensional algebras over algebraically closed fields, we consider two fundamental classes of modules and their geometric counterparts: bricks and $\tau$-rigid modules, as well as brick components and $\tau$-regular components.…

We use the theory of $\textbf{U}_q$-tilting modules to construct cellular bases for centralizer algebras. Our methods are quite general and work for any quantum group $\textbf{U}_q$ attached to a Cartan matrix and include the non-semisimple…

Our approach establishes a natural correspondence between complete orthomodular lattices and certain types of quantales. Firstly, given a complete orthomodular lattice X, we associate with it a Foulis quantale Lin(X) consisting of its…

We consider tilting mutations of a weakly symmetric algebra at a subset of simple modules, as recently introduced by T. Aihara. These mutations are defined as the endomorphism rings of certain tilting complexes of length 1. Starting from a…

We discuss applications of exact structures and relative homological algebra to the study of invariants of multiparameter persistence modules. This paper is mostly expository, but does contain a pair of novel results. Over finite posets,…

Let $B$ be an one-point extension of a finite dimensional $k$-algebra $A$ by a simple $A$-module at a source point $i$. In this paper, we classify the $\tau$-tilting modules over $B$. Moreover, it is shown that there are equations $$|\tilt…

Let $\A$ be a unital separable nuclear $C^*$--algebra which belongs to the bootstrap category $\N$ and $\B$ be a separable stable $C^*$--algebra. In this paper, we consider the group $\Ext_u(\A,\B)$ consisting of the unitary equivalence…

The metohod of ortogonal rotations introduced in the previous papers of the author is used for construction of the explicit form the generators of the simple roots for quantum (and ussual) semisimple algebras. All calculations are presented…

Let $R$ be an associative ring with 1, $G=GL(n, R)$ be the general linear group of degree $n\ge 3$ over $R$. In this paper we calculate the relative centralisers of the relative elementary subgroups or the principal congruence subgroups,…

If two cluster-tilting objects of an acyclic cluster category are related by a mutation, then their endomorphism algebras are nearly-Morita equivalent [Buan-Marsh-Reiten], i.e. their module categories are equivalent "up to a simple module".…