Degenerations of Filippov algebras

Degenerations of nilpotent Lie algebras

In this paper we study degenerations of nilpotent Lie algebras. If λ, μ are two points in the variety of nilpotent Lie algebras, then λ is said to degenerate to μ , λ→deg μ , if μ lies in the Zariski closure of the orbit of λ . It is known that all degenerations of nilpotent Lie algebras of dimension n < 7 can be realized via a one-parameter subgroup. We construct degenerations between characte...

Degenerations of 7-dimensional Nilpotent Lie Algebras

We study the varieties of Lie algebra laws and their subvarieties of nilpotent Lie algebra laws. We classify all degenerations of (almost all) five-step and six-step nilpotent seven-dimensional complex Lie algebras. One of the main tools is the use of trivial and adjoint cohomology of these algebras. In addition, we give some new results on the varieties of complex Lie algebra laws in low dimen...

amenability of banach algebras

chapters 1 and 2 establish the basic theory of amenability of topological groups and amenability of banach algebras. also we prove that. if g is a topological group, then r (wluc (g)) (resp. r (luc (g))) if and only if there exists a mean m on wluc (g) (resp. luc (g)) such that for every wluc (g) (resp. every luc (g)) and every element d of a dense subset d od g, m (r)m (f) holds. chapter 3 inv...

On minimal disjoint degenerations of modules over tame path algebras

For representations of tame quivers the degenerations are controlled by the dimensions of various homomorphism spaces. Furthermore, there is no proper degeneration to an indecomposable. Therefore, up to common direct summands, any minimal degeneration from M to N is induced by a short exact sequence 0 → U → M → V → 0 with indecomposable ends that add up to N . We study these ’building blocs’ of...

Degenerations for Modules over Representation-finite Biserial Algebras