Document Type
Article
Publication Date
8-29-2024
Abstract
We introduce a quotient of the Fomin-Kirillov algebra F K(n) denoted by F KCn (n), over the ideal generated by the edges of a complete graph on n vertices that are missing in the n-cycle graph Cn. In this quotient algebra, we establish a one-to-one correspondence between the basis elements and the set of matchings in an n-cycle graph. We prove that the Hilbert series of F KCn (n) corresponds to the q-Lucas polynomials, and the dimension of this quotient algebra is equal to the Lucas number Ln. We also find the character map of this quotient algebra over the Dihedral group Dn.
Recommended Citation
Homayouni, S. (2024). A quotient of Fomin-Kirillov algebra and Q-Lucas polynomial. Contrib Pure Appl Math, 2(1): 109. doi: https://doi.org/10.33790/cpam1100109.
Comments
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