๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Quasigroup Homogeneous Spaces and Linear Representations

โœ Scribed by Jonathan D.H Smith

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
84 KB
Volume
241
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

โœฆ Synopsis

Using pseudoinverses of incidence matrices of finite quasigroups in partitions induced by left multiplications of subquasigroups, a quasigroup homogeneous space is defined as a set of Markov chain actions indexed by the quasigroup. A certain non-unital ring is afforded a linear representation by a quasigroup homogeneous space. If the quasigroup is a group, the linear representation is a factor in the usual linear representation of the group algebra afforded by the group homogeneous space. In the general case, the structure of the non-unital ring is analyzed in terms of the permutation action of the multiplication group of the quasigroup. The linear representation corestricts to the natural projection of the non-unital ring onto the quotient by its Jacobson radical.

๐Ÿ“œ SIMILAR VOLUMES

Homogeneous and Ultrahomogeneous Linear
Homogeneous and Ultrahomogeneous Linear Spaces
โœ Alice Devillers; Jean Doyen ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 152 KB

If every isomorphism from S$ to S" can be extended to an automorphism of S, S is called ultrahomogeneous. We give a complete classification of all homogeneous (resp. ultrahomogeneous) linear spaces, without making any finiteness assumption on the number of points of S.

Quasi Constricted Linear Representations
Quasi Constricted Linear Representations of Abelian Semigroups on Banach Spaces
โœ Eduard Yu. Emel'yanov; Manfred P. H. Wolff ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 174 KB ๐Ÿ‘ 2 views

Let (X, โ€ข ) be a Banach space. We study asymptotically bounded quasi constricted representations of an abelian semigroup IP in L(X), i. e. representations (Tt) tโˆˆIP which satisfy the following conditions: i) lim tโ†’โˆž Ttx < โˆž for all x โˆˆ X. ii) X 0 := {x โˆˆ X : lim tโ†’โˆž Ttx = 0} is closed and has finite