In this article, the approximate amenability of semigroup algebra e1（S） is investigated, where S is a uniformly locally finite inverse semigroup. Indeed, we show that for a uniformly locally finite inverse semigroup...In this article, the approximate amenability of semigroup algebra e1（S） is investigated, where S is a uniformly locally finite inverse semigroup. Indeed, we show that for a uniformly locally finite inverse semigroup S, the notions of amenability, approximate amenability and bounded approximate amenability of e1（S） are equivalent. We use this to give a direct proof of the approximate amenability of e1 （S） for a Brandt semigroup S. Moreover, we characterize the approximate amenability of e1（S）, where S is a uniformly locally finite band semigroup.展开更多
Our first purpose in this paper is to provide necessary conditions for a weak＊-closed translation invariant subspace in the semigroup algebra of a locally compact topological foundation semigroup to be completely com...Our first purpose in this paper is to provide necessary conditions for a weak＊-closed translation invariant subspace in the semigroup algebra of a locally compact topological foundation semigroup to be completely complemented. We give conditions when a weak＊-closed left translation invariant subspace in Ma,（S）＊ of a compact cancellative foundation semigroup S is the range of a weak＊-weak＊ continuous projection on M~,（S）＊ commuting with translations. Let G be a locally compact group and A be a Banach G-module. Our second purpose in this paper is to study some projections on A＊ and /3（A＊） which commutes with translations and convolution.展开更多
A finite GrSbner-Shirshov basis is constructed for the plactic algebra of rank 3 over a field K. It is also shown that plactic algebras of rank exceeding 3 do not have finite GrSbner-Shirshov bases associated to the n...A finite GrSbner-Shirshov basis is constructed for the plactic algebra of rank 3 over a field K. It is also shown that plactic algebras of rank exceeding 3 do not have finite GrSbner-Shirshov bases associated to the natural degree-lexicographic ordering on the corresponding free algebra. The latter is in contrast with the case of a strongly related class of algebras, called Chinese algebras.展开更多
Let δ be a locally compact semigroup, w be a weight function on δ, and Ma （δ, ω） be the weighted semigroup algebra of δ. Let L0^∞（δ; Ma（δ, ω）） be the C＊-algebra of all Ma（δ, w）-measurable functions ...Let δ be a locally compact semigroup, w be a weight function on δ, and Ma （δ, ω） be the weighted semigroup algebra of δ. Let L0^∞（δ; Ma（δ, ω）） be the C＊-algebra of all Ma（δ, w）-measurable functions g on δ such that g/w vanishes at infinity. We introduce and study a strict topologyβ1 （δ, ω） on Ma（δ, ω） and show that the Banach space L0^∞（6;Ma（δ, ω） can be identified with the dual of Ma（δ, ω） endowed with 31（δ, ω）. We finally investigate some properties of the locally convex topology β^1（δ, ω） on Mo（δ, ω）. Keywords Foundation semigroup, locally convex space, weighted semigroup algebra, strict topology展开更多
We study two-dimensional irreducible projective smooth algebraic semigroups. Minimal surface semigroups with Kodaira dimension at most one are partially classified. We also calculate the local dimension of the moduli ...We study two-dimensional irreducible projective smooth algebraic semigroups. Minimal surface semigroups with Kodaira dimension at most one are partially classified. We also calculate the local dimension of the moduli scheme parameterizing all algebraic semigroup laws on a fixed minimal surface.展开更多
文摘In this article, the approximate amenability of semigroup algebra e1（S） is investigated, where S is a uniformly locally finite inverse semigroup. Indeed, we show that for a uniformly locally finite inverse semigroup S, the notions of amenability, approximate amenability and bounded approximate amenability of e1（S） are equivalent. We use this to give a direct proof of the approximate amenability of e1 （S） for a Brandt semigroup S. Moreover, we characterize the approximate amenability of e1（S）, where S is a uniformly locally finite band semigroup.
文摘Our first purpose in this paper is to provide necessary conditions for a weak＊-closed translation invariant subspace in the semigroup algebra of a locally compact topological foundation semigroup to be completely complemented. We give conditions when a weak＊-closed left translation invariant subspace in Ma,（S）＊ of a compact cancellative foundation semigroup S is the range of a weak＊-weak＊ continuous projection on M~,（S）＊ commuting with translations. Let G be a locally compact group and A be a Banach G-module. Our second purpose in this paper is to study some projections on A＊ and /3（A＊） which commutes with translations and convolution.
文摘A finite GrSbner-Shirshov basis is constructed for the plactic algebra of rank 3 over a field K. It is also shown that plactic algebras of rank exceeding 3 do not have finite GrSbner-Shirshov bases associated to the natural degree-lexicographic ordering on the corresponding free algebra. The latter is in contrast with the case of a strongly related class of algebras, called Chinese algebras.
文摘Let δ be a locally compact semigroup, w be a weight function on δ, and Ma （δ, ω） be the weighted semigroup algebra of δ. Let L0^∞（δ; Ma（δ, ω）） be the C＊-algebra of all Ma（δ, w）-measurable functions g on δ such that g/w vanishes at infinity. We introduce and study a strict topologyβ1 （δ, ω） on Ma（δ, ω） and show that the Banach space L0^∞（6;Ma（δ, ω） can be identified with the dual of Ma（δ, ω） endowed with 31（δ, ω）. We finally investigate some properties of the locally convex topology β^1（δ, ω） on Mo（δ, ω）. Keywords Foundation semigroup, locally convex space, weighted semigroup algebra, strict topology
文摘We study two-dimensional irreducible projective smooth algebraic semigroups. Minimal surface semigroups with Kodaira dimension at most one are partially classified. We also calculate the local dimension of the moduli scheme parameterizing all algebraic semigroup laws on a fixed minimal surface.
