Related papers: Super Morita Theory
A notion of a split quasi-hereditary algebra has been defined by Cline, Parshall and Scott. Du and Rui describe a based approach to split quasi-hereditary algebras. We develop this approach further to show that over a complete local…
We develop basic notions and methods of algebraic geometry over the algebraic objects called hyperrings. Roughly speaking, hyperrings generalize rings in such a way that an addition is `multi-valued'. This paper largely consisits of two…
The book is devoted to investigation of arithmetic of the matrix rings over certain classes of commutative finitely generated principal ideals domains. We mainly concentrate on constructing of the matrix factorization theory. We reveal a…
We introduce the notion of $\Delta$ and $\sigma\,\Delta-$ pairs for operator algebras and characterise $\Delta-$ pairs through their categories of left operator modules over these algebras. Furthermore, we introduce the notion of…
Partial Galois extensions were recently introduced by Dokuchaev, Ferrero and Paques. We introduce partial Galois extensions for noncommutative rings, using the theory of Galois corings. We associate a Morita context to a partial action on a…
In this paper we determine the complex generic representation theory of the Juyumaya algebra. We show that a certain specialization of this algebra is isomorphic to the small ramified partition algebra, introduced by P. Martin.
We study a topological generalization of ideal co-maximality in topological rings and present some of its properties, including a generalization of the Chinese remainder theorem. Using the hyperspace uniformity, we prove a stronger version…
We consider the group algebra of the symmetric group as a superalgebra, and describe its Lie subsuperalgebra generated by the transpositions. The updated version corrects some of the arguments made in Sections 4.5 - 4.7. The statements of…
We extend a conjugacy Theorem of Cartan subalgebras, originally established for symmetrizable Kac-Moody algebras, to the broader context of affine Kac-Moody superalgebras. Along the way, we obtain several results that deepen our…
In these proceedings for the First School on Field Theory and Gravitation (Vit\'oria, Brasil), a brief introduction is given to superstring theory and its duality symmetries. This introduction is intended for beginning graduate students…
Nuclear supersymmetry is reviewed and some of its applications and extensions are discussed, together with a proposal for new, more stringent and precise tests to probe the supersymmetry classification, in particular, correlations between…
We extend the theory of fast Fourier transforms on finite groups to finite inverse semigroups. We use a general method for constructing the irreducible representations of a finite inverse semigroup to reduce the problem of computing its…
In these lectures I present a basic introduction to supersymmetry, especially to N=1 supersymmetric gauge theories and their renormalization, in the Wess-Zumino gauge. I also discuss the various ways supersymmetry may be broken in order to…
A relationship between coseparable corings and separable non-unital rings is established. In particular it is shown that an A-coring C has an associative A-balanced product. A Morita context is constructed for a coseparable coring with a…
In this talk I will survey some of the basic facts about superstring theories in 10 dimensions and the dualities that relate them to M theory in 11 dimensions. Then I will mention some important unresolved issues.
We describe Morita equivalence of unital locally matrix algebras in terms of their Steinitz parametrization. Two countable dimensional unital locally matrix algebras are Morita equivalent if and only if their Steinitz numbers are rationally…
In this letter we give an overview on recent developments in representation theory of star product algebras. In particular, we relate the *-representation theory of *-algebras over rings C = R(i) with an ordered ring R and i^2 = -1 to the…
Let $L$ be a solvable Lie algebra of dimension less than or equal to 4 over finite fields. We compute and record, in explicit symbolic form, the zeta functions enumerating subalgebras or ideals of $L$, and study their properties. We also…
We construct a generalization of Koszul duality in the sense of Keller--Lef\`evre for not necessarily augmented algebras. This duality is closely related to classical Morita duality and specializes to it in certain cases.
We continue the study of cluster algebras initiated in math.RT/0104151 and math.RA/0208229. We develop a new approach based on the notion of an upper cluster algebra, defined as an intersection of certain Laurent polynomial rings.…