We establish several properties of a quadratic algebra over a field k, which is a deformation of the symmetric algebra Sk³. In particular, we prove that A is an integral domain, noetherian and Koszul; we compute its first Hochschild cohomology group; we determine the corresponding Poisson structure on k³ and its symplectic leaves; we define an involution on A and describe the corresponding irreducible involutive representations.
2000 Mathematics Subject Classification: Primary 20C07, 20K10, 20K20, 20K21; Secondary 16U60, 16S34.Let PG be the abelian modular group ring of the abelian group G over the abelian ring P with 1 and prime char P = p. In the present article,the p-primary components Up(PG) and S(PG) of the groups of units U(PG) and V(PG) are classified for some major classes of abelian groups. Suppose K is a first kind field with respect to p in char K ≠ p and A is an abelian p-group. In the present work, the p-primary...
Let and be two ring homomorphisms and let and be two ideals of and , respectively, such that . We investigate unipotent, symmetric and reversible properties of the bi-amalgamation ring of with along with respect to .
By an extension algebra of a finite-dimensional K-algebra A we mean a Hochschild extension algebra of A by the dual A-bimodule . We study the problem of when extension algebras of a K-algebra A are symmetric. (1) For an algebra A= KQ/I with an arbitrary finite quiver Q, we show a sufficient condition in terms of a 2-cocycle for an extension algebra to be symmetric. (2) Let L be a finite extension field of K. By using a given 2-cocycle of the K-algebra L, we construct a 2-cocycle of the K-algebra...
We classify (up to Morita equivalence) all symmetric special biserial algebras of Euclidean type, by algebras arising from Brauer graphs.
On décrit une approche homologique des systèmes dynamiques contraints. Cette approche, directement inspirée des travaux de D. McMullan et de M. Henneaux concernant le formalisme de Batalin, Fradkin et Vilkovisky, contient une interprétation des fantômes et de leurs conjugués. Dans le cadre des systèmes dans l’espace des phases, la construction se fait en deux étapes. La première étape consiste à construire une algèbre différentielle graduée dont la cohomologie en degré zéro est l’espace des observables...