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Sur une algèbre Q-symétrique

A. Guichardet (1997)

Annales Polonici Mathematici

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.

Sylow P-Subgroups of Abelian Group Rings

Danchev, P. (2003)

Serdica Mathematical Journal

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...

Symmetric and reversible properties of bi-amalgamated rings

Antonysamy Aruldoss, Chelliah Selvaraj (2024)

Czechoslovak Mathematical Journal

Let f : A B and g : A C be two ring homomorphisms and let K and K ' be two ideals of B and C , respectively, such that f - 1 ( K ) = g - 1 ( K ' ) . We investigate unipotent, symmetric and reversible properties of the bi-amalgamation ring A f , g ( K , K ' ) of A with ( B , C ) along ( K , K ' ) with respect to ( f , g ) .

Symmetric Hochschild extension algebras

Yosuke Ohnuki, Kaoru Takeda, Kunio Yamagata (1999)

Colloquium Mathematicae

By an extension algebra of a finite-dimensional K-algebra A we mean a Hochschild extension algebra of A by the dual A-bimodule H o m K ( A , K ) . 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...

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