Geodesic
Quadratic algebras with few relations
Glasgow mathematical journal, Tome 39 (1997) no. 3, pp. 323-332

Voir la notice de l'article provenant de la source Cambridge University Press

Throughout V will be a finite dimensional vector space over a field k and T(V) will denote the tensor algebra over V. For simplicity the symbol ⊗ will be omitted in the writing of the elements of T(V). Let be a basis of V ordered by Xi<Xi+1 for all i. Then we order the non-commutative monomials and 1 ≤ is ≤ n for s = 1,..., l} lexicographically from the left. D. Anick [1, p. 652] defines the high term of an element b in T(V) to be the highest monomial appearing in b. As a consequence of [1,3.2], if the set of the high terms of homogeneous relations is combinatorically free in the sense of no overlap ambiguities, then the connected algebra has global dimension 2. The purpose of this note is to prove this result and more for quadratic algebras under other hypotheses on the relations. 
Zhang, James J. Quadratic algebras with few relations. Glasgow mathematical journal, Tome 39 (1997) no. 3, pp. 323-332. doi: 10.1017/S0017089500032249
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