Bibliographic Details
| Title: |
Structure of free semigroupoid algebras. |
| Authors: |
Davidson, Kenneth R.1 (AUTHOR) krdavids@uwaterloo.ca, Dor-On, Adam1,2 (AUTHOR) adoron@illinois.edu, Li, Boyu1,3 (AUTHOR) boyuli@uvic.ca |
| Source: |
Journal of Functional Analysis. Nov2019, Vol. 277 Issue 9, p3283-3350. 68p. |
| Subjects: |
Semigroup algebras, Algebra, Structural analysis (Engineering), Mathematical equivalence, Reflexivity |
| Abstract: |
A free semigroupoid algebra is the wot -closure of the algebra generated by a TCK family of a graph. We obtain a structure theory for these algebras analogous to that of free semigroup algebra. We clarify the role of absolute continuity and wandering vectors. These results are applied to obtain a Lebesgue-von Neumann-Wold decomposition of TCK families, along with reflexivity, a Kaplansky density theorem and classification for free semigroupoid algebras. Several classes of examples are discussed and developed, including self-adjoint examples and a classification of atomic free semigroupoid algebras up to unitary equivalence. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
