Poset topology and homological invariants of algebras arising in algebraic combinatorics. (English. French summary) Zbl 1394.16004
Proceedings of the 26th international conference on formal power series and algebraic combinatorics, FPSAC 2014, Chicago, IL, USA, June 29 – July 3, 2014. Nancy: The Association. Discrete Mathematics & Theoretical Computer Science (DMTCS). Discrete Mathematics and Theoretical Computer Science. Proceedings, 71-82 (2014).
Summary: We present a beautiful interplay between combinatorial topology and homological algebra for a class of monoids that arise naturally in algebraic combinatorics. We explore several applications of this interplay. For instance, we provide a new interpretation of the Leray number of a clique complex in terms of non-commutative algebra.
For the entire collection see [Zbl 1298.05004].
For the entire collection see [Zbl 1298.05004].
MSC:
| 16E30 | Homological functors on modules (Tor, Ext, etc.) in associative algebras |
| 05E15 | Combinatorial aspects of groups and algebras (MSC2010) |
| 16G10 | Representations of associative Artinian rings |
| 20M99 | Semigroups |
| 52C35 | Arrangements of points, flats, hyperplanes (aspects of discrete geometry) |
