Relative invariants of quivers of tame type

Tame Quivers and Affine Enveloping Algebras

Let g be an affine Kac-Moody algebra with symmetric Cartan datum, n be the maximal nilpotent subalgebra of g. By the Hall algebra approach, we construct integral bases of the Z-form of the enveloping algebra U(n). In particular, the representation theory of tame quivers is essentially used in this paper.

Invariants of Mixed Representations of Quivers I

Semi-invariants of 2-representations of Quivers

In this work we obtain a version of the Procesi-Rasmyslov Theorem for the algebra of semi-invariants of representations of an arbitrary quiver with dimension vector (2, 2, . . . , 2).

Semi-invariants of mixed representations of quivers

The notion of mixed representations of quivers can be derived from ordinary quiver representations by considering the dual action of groups on “vertex” vector spaces together with the usual action. A generating system for the algebra of semi-invariants of mixed representations of a quiver is determined. This is done by reducing the problem to the case of bipartite quivers of the special form an...

Semi-invariants of ∗-representations of quivers

The notion of ∗-representations of quivers can be obtained from ordinary quiver representations by considering coaction of groups on “vertex” vector spaces together with action. A generating system for the algebra of semiinvariants of ∗-representations of a quiver is determined. This was done by reducing the problem to the case of bipartite quivers of the special form and by introducing a funct...