Koszul calculus of preprojective algebras

Actually, we check in Section 5 that for nilpotent Lie algebras over a field of characteristic zero, up to dimension 9 the reduced Koszul map is always zero (by reduction to

We have seen above that the Chevalley-Eilenberg complex of L (with homological grading) is a resolution of A, and the Chevalley-Eilenberg complexes of L ≥2 and L ≥3 calculate

Abstract. In this article we give a conceptual definition of Manin products in any category endowed with two coherent monoidal products. This construction can be applied to

To study algebraic structures defined by operations with multiple inputs and multiple outputs, like bialgebras or Lie bialgebras for instance, one needs to generalize the notion

Assume that k is a field and that ¯ A is a positively graded k-algebra. We say that A ¯ is Koszul if each simple graded module which is pure of weight 0 has a linear

For the definition of Calabi-Yau algebras, we refer to Ginzburg [7]. The following is a higher Hochschild cohomology version of Poincar´ e duality, and it is based on the

Throughout the paper, the algebras of this class will be denoted by A, sometimes A(f ) or A(M ) if we want to specify the na¨ıve non-commutative quadric which is just a

The action of G on a path algebra kQ permuting the primitive idempotents and stabilizing the linear subspace of kQ spanned by the arrows induces naturally an action of G on kQ and Q..