LetG be a finite p-group,K a field of characteristic p, and J the radical of the group algebra K[G]. We study modular representations using some new results of the theory of extensions of modules. More precisely, we describe the K[G]-modules M such that J2M = 0 and give some properties and isomorphism invariants which allow us to compute the number of isomorphism classes of K[G]-modulesM such t...

We construct a numeric algorithm for completing the proof of conjecture asserting that all deformed preprojective algebras generalized Dynkin type are periodic. In particular, we obtain an algorithmic procedure showing non-trivial types E7 and E8 exist only in characteristic 2. As consequence, show E6, periodic classification such algebras, up to algebra isomorphism. do it by reduction solution...

The isomorphism problem for centrally nilpotent loops can be tackled by methods of cohomology. We develop tools based on cohomology and linear algebra that either lend themselves to direct count of the isomorphism classes (notably in the case of nilpotent loops of order 2q, q a prime), or lead to efficient classification computer programs. This allows us to enumerate all nilpotent loops of orde...

We describe the use of symbolic algebraic computation allied with AI search techniques, applied to the problem of the identification, enumeration and storage of all monoids of order 9 or less. Our approach is novel, using computer algebra to break symmetry and constraint satisfaction search to find candidate solutions. We present new results in algebraic combinatorics: up to isomorphism and ant...

Since 1999 it became obvious that the would be 'isomorphism' between the affinê sl(2) algebra and the N=2 superconformal algebras, proposed by some authors, simply does not work. However, this issue was never properly discussed in the literature and, as a result, some confusion still remains. In this article we finally settle down, clearly and unambiguously, the true facts: there is no isomorph...

Given a variety V of universal algebras. A new approach is suggested to characterize algebraically automorphisms of the category of free V-algebras. It gives in many cases an answer to the problem set by the first of authors, if automorphisms of such a category are inner or not. This question is important for universal algebraic geometry [5, 9]. Most of results will actually be proved to hold f...

Assume A is a Fréchet algebra equipped with a smooth isometric action of a vector group V , and consider Rieffel’s deformation AJ of A. We construct an explicit isomorphism between the smooth crossed products V n AJ and V n A. When combined with the Elliott-Natsume-Nest isomorphism, this immediately implies that the periodic cyclic cohomology is invariant under deformation. Specializing to the ...

Abstract Let G be a finite group, let A an infinite-dimensional stably simple unital C*-algebra, and $\alpha \colon \to {\operatorname {Aut}} (A)$ action of on which has the weak tracial Rokhlin property. $A^{\alpha }$ fixed point algebra. Then radius comparison satisfies ${\operatorname {rc}} (A^{\alpha }) \leq ( C^* (G, A, \alpha ) ({1}/{{{\operatorname{card}}} (G))} \cdot . The inclusion in ...

Motivated by the relation between Schur algebra and group of a symmetric group, along with other similar examples in algebraic Lie theory, Min Fang Steffen Koenig [15], [16] addressed some behaviour endomorphism generator over algebra, which they called gendo-symmetric algebra. Continuing this line works, we classify article representation-finite algebras that have precisely one isomorphism cla...

Let k be a perfect field and let K/k be a finite extension of fields. An arithmetic noncommutative projective line is a noncommutative space of the form ProjSK(V ), where V be a k-central two-sided vector space over K of rank two and SK(V ) is the noncommutative symmetric algebra generated by V over K defined by M. Van den Bergh [26]. We study the geometry of these spaces. More precisely, we pr...