Compact group actions on operator algebras and their spectra

Compact Quantum Group Actions on C*-algebras and Invariant Derivations

We define the notion of invariant derivation of a C*-algebra under a compact quantum group action and prove that in certain conditions, such derivations are generators of one parameter automorphism groups.

Compact weighted Frobenius-Perron operators and their spectra

In this note we characterize the compact weighted Frobenius-Perron operator $p$ on $L^1(Sigma)$ and determine their spectra. We also show that every weakly compact weighted Frobenius-Perron operator on $L^1(Sigma)$ is compact.

Lie group actions on compact

Let G be a homotopically trivial and effective compact Lie group action on a compact manifold N of nonpositive curvature. Under certain assumptions on N we prove that if G has dimension equal to rank of Center π1(N), then G must be connected. Furthermore, if on N there exists a point having negative definite Ricci tensor, then we show that G is the trivial group.

Group Actions on Algebras and Module Categories

Let k be a field and A a finite dimensional (associative with 1) k-algebra. By modA we denote the category of finite dimensional left A-modules. In many important situations we may suppose that A is presented as a quiver with relations (Q, I) (e.g. if k is algebraically closed, then A is Morita equivalent to kQ/I). We recall that if A is presented by (Q, I), then Q is a finite quiver and I is a...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras