Author:
Pluta Robert,Russo Bernard
Abstract
AbstractWe are interested in properties, especially injectivity (in the sense of category theory), of the ternary rings of operators generated by certain subsets of an inverse semigroup via the regular representation. We determine all subsets of the extended bicyclic semigroup which are closed under the triple product $$xy^*z$$
x
y
∗
z
(called semiheaps) and show that the weakly closed ternary rings of operators generated by them are injective operator spaces.
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory
Reference16 articles.
1. Daviaud, L., Johnson, M., Kambites, M.: Identities in upper triangular tropical matrix semigroups and the bicyclic monoid. J. Algebra 501, 503–525 (2018)
2. Descalço, L., Rus̆kuc, N.: Subsemigroups of the bicyclic monoid. Int. J. Algebra Comput. 15(1), 37–57 (2005)
3. Effros, E.G., Ozawa, N., Ruan, Z.-J.: On injectivity and nuclearity for operator spaces. Duke Math. J. 110(3), 489–522 (2001)
4. Hestenes, M.R.: A ternary algebra with applications to matrices and linear transformations. Arch. Rational Mech. Anal. 11, 138–194 (1962)
5. Hollings, C.D.: Mathematics Across the Iron Curtain. A History of the Algebraic Theory of Semigroups. American Mathematical Society, Providence (2014)