Files and links (1)
SubmittedOpen Access (License Unspecified), Open
Journal article
Subalgebras of the Fomin-Kirillov algebra
Journal of algebraic combinatorics, v 44(3), pp 785-829
01 Nov 2016
Abstract
The Fomin-Kirillov algebra epsilon(n) is a noncommutative quadratic algebra with a generator for every edge of the complete graph on n vertices. For any graph G on n vertices, we define epsilon(G) to be the subalgebra of epsilon(n) generated by the edges of G. We show that these algebras have many parallels with Coxeter groups and their nil-Coxeter algebras: for instance, epsilon(G) is a free epsilon(H)-module for any H subset of G, and if epsilon(G) is finite-dimensional, then its Hilbert series has symmetric coefficients. We determine explicit monomial bases and Hilbert series for epsilon(G) when G is a simply laced finite Dynkin diagram or a cycle, in particular showing that epsilon(G) is finite-dimensional in these cases. We also present conjectures for the Hilbert series of epsilon((D) over barn), epsilon((E) over bar6), and epsilon((E) over bar7), as well as the graphs G on six vertices for which epsilon(G) is finite-dimensional.
Metrics
Details
- Title
- Subalgebras of the Fomin-Kirillov algebra
- Creators
- Jonah Blasiak - Drexel UniversityRicky Ini Liu - North Carolina State UniversityKarola Meszaros - Cornell University
- Publication Details
- Journal of algebraic combinatorics, v 44(3), pp 785-829
- Publisher
- Springer Nature
- Number of pages
- 45
- Grant note
- DMS 1161280; DMS 1004375; DMS 1103933 / NSF; National Science Foundation (NSF)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000387223000010
- Scopus ID
- 2-s2.0-84966701500
- Other Identifier
- 991019168416004721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics