Cyclotomic and Littlewood Polynomials Associated to Algebras
Let A be a finite dimensional algebra over an algebraically closed field k . Assume A is a basic connected and triangular algebra with n pairwise non-isomorphic simple modules. We consider the Coxeter transformation ϕ A T as the automorphism of the Grothendieck group K 0 A induced by the Auslander-R...
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| LEADER | 01798 am a22001933u 4500 | ||
|---|---|---|---|
| 001 | intechopen_books_8599 | ||
| 042 | |a dc | ||
| 100 | 1 | 0 | |a de la Peña, José-Antonio |e author |
| 245 | 0 | 0 | |a Cyclotomic and Littlewood Polynomials Associated to Algebras |
| 260 | |b IntechOpen, |c 2019-04-06. | ||
| 500 | |a https://mts.intechopen.com/articles/show/title/cyclotomic-and-littlewood-polynomials-associated-to-algebras | ||
| 520 | |a Let A be a finite dimensional algebra over an algebraically closed field k . Assume A is a basic connected and triangular algebra with n pairwise non-isomorphic simple modules. We consider the Coxeter transformation ϕ A T as the automorphism of the Grothendieck group K 0 A induced by the Auslander-Reiten translation τ in the derived category D b mod A of the module category mod A of finite dimensional left A -modules. In this paper we study the Mahler measure M χ A of the Coxeter polynomial χ A of certain algebras A . We consider in more detail two cases: (a) A is said to be cyclotomic if all eigenvalues of χ A are roots of unity; (b) A is said to be of Littlewood type if all coefficients of χ A are − 1 , 0 or 1 . We find criteria in order that A is of one of those types. In particular, we establish new records according to Mossingshoff's list of Record Mahler measures of polynomials q with 1 < M q as small as possible, ordered by their number of roots outside the unit circle. | ||
| 540 | |a https://creativecommons.org/licenses/by/3.0/ | ||
| 546 | |a en | ||
| 690 | |a Polynomials - Theory and Application | ||
| 655 | 7 | |a Chapter, Part Of Book |2 local | |
| 786 | 0 | |n https://www.intechopen.com/books/8599 | |
| 787 | 0 | |n ISBN:978-1-83880-269-1 | |
| 856 | \ | \ | |u https://mts.intechopen.com/articles/show/title/cyclotomic-and-littlewood-polynomials-associated-to-algebras |z Get Online |