The Gelfand-Kirillov dimension of quadratic algebras satisfying the cyclic condition |
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Authors: | Ferran Cedó Eric Jespers Jan Okninski |
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Affiliation: | Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain ; Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium ; Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland |
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Abstract: | We consider algebras over a field presented by generators and subject to square-free relations of the form with every monomial , appearing in one of the relations. It is shown that for the Gelfand-Kirillov dimension of such an algebra is at least two if the algebra satisfies the so-called cyclic condition. It is known that this dimension is an integer not exceeding . For , we construct a family of examples of Gelfand-Kirillov dimension two. We prove that an algebra with the cyclic condition with generators has Gelfand-Kirillov dimension if and only if it is of -type, and this occurs if and only if the multiplicative submonoid generated by is cancellative. |
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