Topologically $Q$-algebras, more

Topologically Left Invariant Mean on Dual Semigroup Algebras

Banach algebras of topologically bounded index

We consider normed and Banach algebras satisfying a condition topologically analogous to bounded index for rings. We investigate stability properties, prove a topological version of a theorem of Jacobson, and find in many cases co-incidence with well-known finiteness properties.

Topologically left invariant means on semigroup algebras

Let M(S) be the Banach algebra of all bounded regular Borel measures on a locally compact Hausdorff semitopological semigroup S with variation norm and convolution as multiplication. We obtain necessary and sufficient conditions for M(S)∗ to have a topologically left invariant mean.

1 Introduction Q-algebras

where 1 denotes the universal relation on the base set. These Q-operations have a geometrical origin, but in [Jónsson 1991] Jónsson discusses them only in a context where he compares the expressive power of various clones of operations on binary relations. For instance, the operation defined in the picture above does not belong to the Tarski clone; that is, Q cannot be defined by using the bool...

GRADED q-SCHUR ALGEBRAS

Generalizing recent work of Brundan and Kleshchev, we introduce grading on Dipper-James’ q-Schur algebra, and prove a graded analogue of the Leclerc and Thibon’s conjecture on the decomposition numbers of the q-Schur algebra.