کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4584859 | 1630511 | 2014 | 27 صفحه PDF | دانلود رایگان |
Assume that X={x1,…,xg}X={x1,…,xg} is a finite alphabet and K is a field. We study monomial algebras A=K〈X〉/(W)A=K〈X〉/(W), where W is an antichain of Lyndon words in X of arbitrary cardinality. We find a Poincaré–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 d−1⩽|W|⩽d(d−1)/2d−1⩽|W|⩽d(d−1)/2. Furthermore, A has polynomial growth iff the set of Lyndon atoms N is finite. In this case A has a K -basis N={l1α1l2α2⋯ldαd|αi⩾0,1⩽i⩽d}, where N={l1,…,ld}N={l1,…,ld}. We give an extremal class of monomial algebras, the Fibonacci–Lyndon algebras, FnFn, with global dimension n and polynomial growth, and show that the algebra F6F6 of global dimension 6 cannot be deformed, keeping the multigrading, to an Artin–Schelter regular algebra.
Journal: Journal of Algebra - Volume 403, 1 February 2014, Pages 470–496