Su, Hao Yang, Dong
Published in
Algebras and Representation Theory

Given an elementary simple-minded collection in the derived category of a non-positive dg algebra with finite-dimensional total cohomology, we construct a silting object via Koszul duality.

Feickert, Aaron J. Sather-Wagstaff, Sean
Published in
Algebras and Representation Theory

Over a noetherian ring, it is a classic result of Matlis that injective modules admit direct sum decompositions into injective hulls of quotients by prime ideals. We show that over a Cohen-Macaulay ring admitting a dualizing module, Gorenstein injective modules admit similar filtrations. We also investigate Tor-modules of Gorenstein injective modul...

Arnal, Didier Khlifi, Olfa
Published in
Algebras and Representation Theory

The simple GL(n,ℂ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$GL(n,\mathbb {C})$\end{document}-modules are described by using semistandard Young tableaux. Any semist...

Camacho, L. M. Khudoyberdiyev, A. Kh. Omirov, B. A.
Published in
Algebras and Representation Theory

In this paper we study subalgebras of complex finite dimensional evolution algebras. We obtain the classification of nilpotent evolution algebras whose any subalgebra is an evolution subalgebra with a basis which can be extended to a natural basis of algebra. Moreover, we formulate three conjectures related to the description of such non-nilpotent ...

Chirvasitu, Alexandru Penkov, Ivan
Published in
Algebras and Representation Theory

We introduce (partially) ordered Grothendieck categories and apply results on their structure to the study of categories of representations of the Mackey Lie algebra of infinite matrices 𝔤𝔩MV,V∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...

Lorscheid, Oliver Weist, Thorsten
Published in
Algebras and Representation Theory

In this text, we exhibit the quiver Plücker relations for a quiver Grassmannian and show that they describe the quiver Grassmannian as a closed subscheme of a product of usual Grassmannians.

Rozhkovskaya, Natasha
Published in
Algebras and Representation Theory

We deduce from a determinant identity on quantum transfer matrices of generalized quantum integrable spin chain model their generating functions. We construct the isomorphism of Clifford algebra modules of sequences of transfer matrices and the boson space of symmetric functions. As an application, tau-functions of transfer matrices immediately ari...

Biswas, Indranil Chaput, Pierre-Emmanuel Mourougane, Christophe
Published in
Algebras and Representation Theory

Let G be an almost simple simply-connected affine algebraic group over an algebraically closed field k of characteristic p > 0. If G has type Bn, Cn or F4, we assume that p > 2, and if G has type G2, we assume that p > 3. Let P ⊂ G be a parabolic subgroup. We prove that the tangent bundle of G/P is Frobenius stable with respect to the anticanonical...

Tsymbaliuk, Alexander
Published in
Algebras and Representation Theory

In this paper, we relate the well-known Fock representations of Üq,d(𝔰𝔩n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\ddot {U}_{q,d}(\mathfrak {sl}_{n})$\end{documen...

Khairnar, Anil Waphare, B. N.
Published in
Algebras and Representation Theory

The concept of a central strict ideal in a principally quasi-Baer (p.q.-Baer) ∗-ring is introduced. It is proved that the set of all prime central strict ideals in a p.q.-Baer ∗-ring is an anti-chain with respect to set inclusion. We obtain a separation theorem, which ensures an existence of prime central strict ideals in a p.q.-Baer *-ring. It is ...