1. CMB 2011 (vol 54 pp. 411)
|Operator Algebras with Unique Preduals|
We show that every free semigroup algebra has a (strongly) unique Banach space predual. We also provide a new simpler proof that a weak-$*$ closed unital operator algebra containing a weak-$*$ dense subalgebra of compact operators has a unique Banach space predual.
Keywords:unique predual, free semigroup algebra, CSL algebra
Categories:47L50, 46B04, 47L35
2. CMB 2007 (vol 50 pp. 56)
|Simplicial Cohomology of Some Semigroup Algebras |
In this paper, we investigate the higher simplicial cohomology groups of the convolution algebra $\ell^1(S)$ for various semigroups $S$. The classes of semigroups considered are semilattices, Clifford semigroups, regular Rees semigroups and the additive semigroups of integers greater than $a$ for some integer $a$. Our results are of two types: in some cases, we show that some cohomology groups are $0$, while in some other cases, we show that some cohomology groups are Banach spaces.
Keywords:simplicial cohomology, semigroup algebra
3. CMB 2004 (vol 47 pp. 343)
|Combinatorics of Words and Semigroup Algebras Which Are Sums of Locally Nilpotent Subalgebras |
We construct new examples of non-nil algebras with any number of generators, which are direct sums of two locally nilpotent subalgebras. Like all previously known examples, our examples are contracted semigroup algebras and the underlying semigroups are unions of locally nilpotent subsemigroups. In our constructions we make more transparent than in the past the close relationship between the considered problem and combinatorics of words.
Keywords:locally nilpotent rings,, nil rings, locally nilpotent semigroups,, semigroup algebras, monomial algebras, infinite words
Categories:16N40, 16S15, 20M05, 20M25, 68R15