Monomial algebras defined by Lyndon words

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• 作者：Tatiana Gateva-Ivanova^a ; ^b ; ¹ ; ^{tatianagateva@yahoo.com" class="auth_mail} ; ^{tatyana@aubg.bg" class="auth_mail} ; Gunnar Flø ; ystad^c ; ^{gunnar@mi.uib.no" class="auth_mail}
• 关键词：primary ; 16P90 ; 16S15 ; 18G20 ; 68R15 ; secondary ; 16S80 ; 16Z05
• 刊名：Journal of Algebra
• 出版年：1 February, 2014
• 年：2014
• 卷：403
• 期：Complete
• 页码：470-496
• 全文大小：385 K

文摘

Assume that is a finite alphabet and K is a field. We study monomial algebras , where W is an antichain of Lyndon words in X of arbitrary cardinality. We find a Poincar茅-Birkhoff-Witt type basis of A in terms of its Lyndon atoms N, but, in general, N may be infinite. We prove that if A has polynomial growth of degree d then A has global dimension d and is standard finitely presented, with . Furthermore, A has polynomial growth iff the set of Lyndon atoms N is finite. In this case A has a K-basis , where . We give an extremal class of monomial algebras, the Fibonacci-Lyndon algebras, , with global dimension n and polynomial growth, and show that the algebra of global dimension 6 cannot be deformed, keeping the multigrading, to an Artin-Schelter regular algebra.