We introduce a construction which allows us to identify the elements of the skeletons of a CW-complex P(m) and the monomials in m variables. From this, we infer that there is a bijection between finite CW-subcomplexes of P(m), which are quotients of finite simplicial complexes, and certain bigraded standard Artinian Gorenstein algebras, generalizing previous constructions of Faridi and ourselves. We apply this to a generalization of Nagata idealization for level algebras. These algebras are standard graded Artinian algebras whose Macaulay dual generator is given explicitly as a bigraded polynomial of bidegree (1,d). We consider the algebra associated to polynomials of the same bidegree (d1,d2).
CW-complex Nagata idealizations / Capasso, A.; De Poi, P.; Ilardi, G.. - In: ADVANCES IN APPLIED MATHEMATICS. - ISSN 0196-8858. - 120:(2020), p. 102079. [10.1016/j.aam.2020.102079]
CW-complex Nagata idealizations
Ilardi G.
2020
Abstract
We introduce a construction which allows us to identify the elements of the skeletons of a CW-complex P(m) and the monomials in m variables. From this, we infer that there is a bijection between finite CW-subcomplexes of P(m), which are quotients of finite simplicial complexes, and certain bigraded standard Artinian Gorenstein algebras, generalizing previous constructions of Faridi and ourselves. We apply this to a generalization of Nagata idealization for level algebras. These algebras are standard graded Artinian algebras whose Macaulay dual generator is given explicitly as a bigraded polynomial of bidegree (1,d). We consider the algebra associated to polynomials of the same bidegree (d1,d2).File | Dimensione | Formato | |
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