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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.

The algebra of the subspace semigroup of M ( q )

Jan Okniński (2002)

Colloquium Mathematicae

The semigroup S = S ( M ( q ) ) of subspaces of the algebra M ( q ) of 2 × 2 matrices over a finite field q is studied. The ideal structure of S, the regular -classes of S and the structure of the complex semigroup algebra ℂ[S] are described.

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