Lie and Jordan algebras, their representations and generalizations
Leavitt path algebras, Steinberg algebras and partial actions
Representations of non-associative algebras and superalgebras
| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Hungarian Acad Sci, Renyi Inst Math, Pf 127, H-1364 Budapest - Hungary
[2] VAST, Inst Math, 18 Hoang Quoc Viet, Hanoi - Vietnam
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | ADVANCES IN MATHEMATICS; v. 377, JAN 22 2021. |
| Web of Science Citations: | 0 |
| Abstract | |
Several descriptions of irreducible representations of both Leavitt and hence Cohn path algebras of an arbitrary digraph with coefficients in a commutative field introduced by Chen and Rangaswamy are presented, using both infinite paths on the right and vertices as well as direct limits or factors of cyclic projective ideals of the ordinary quiver algebra. Specific properties of these irreducible representations become immediate when they are viewed as modules over the commutative subalgebras generated by symmetric idempotents of paths, thereby providing a unified way to treat them. Furthermore, their defining relations are read off, whence criteria are easily given when they are finitely presented or finite dimensional. Their endomorphism rings, and annihilator primitive ideals are also computed directly. (C) 2020 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 18/06538-6 - Leavitt path algebras, Steinberg algebras and partial actions |
| Grantee: | Tran Giang Nam |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |