On monomial algebras of finite global dimension

Anick, David J.

doi:10.1090/S0002-9947-1985-0797061-3

On monomial algebras of finite global dimension
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by David J. Anick

Trans. Amer. Math. Soc. 291 (1985), 291-310

DOI: https://doi.org/10.1090/S0002-9947-1985-0797061-3

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Abstract:

Let $G$ be an associative monomial ${\mathbf {k}}$-algebra. If $G$ is assumed to be finitely presented, then either $G$ contains a free subalgebra on two monomials or else $G$ has polynomial growth. If instead $G$ is assumed to have finite global dimension, then either $G$ contains a free subalgebra or else $G$ has a finite presentation and polynomial growth. Also, a graded Hopf algebra with generators in degree one and relations in degree two contains a free Hopf subalgebra if the number of relations is small enough.

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