Open AccessTwisted Toeplitz Algebras of Cyclically Ordered Groups
Author(s) -
Rizky Rosjanuardi,
Sumanang Muhtar Gozali,
Isnie Yusnitha
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1940/1/012015
Subject(s) - cog , mathematics , toeplitz matrix , group (periodic table) , abelian group , pure mathematics , semigroup , algebra over a field , order (exchange) , representation (politics) , regular representation , combinatorics , computer science , physics , finance , quantum mechanics , artificial intelligence , politics , political science , law , economics
We consider the group ℤƗ lex ℤ as a linear ordered abelian group, and we induce a cyclic order so that the group is cyclically ordered, and denote it as ℤƗ COG ℤ. Suppose σ is a 2-cocycle on the group ℤƗ COG ℤ. We construct an isometric representation of the semigroup (ℤƗ COG ℤ). This representation generates a canonical algebra which we call the twisted Toeplitz algebra of the cyclically ordered group ℤƗ COG ℤ.