On Koszul Algebras and a New Construction of Artin-schelter Regular Algebras
نویسندگان
چکیده
We prove the simple fact that the factor ring of a Koszul algebra by a regular, normal, quadratic element is a Koszul algebra. This fact leads to a new construction of quadratic Artin-Schelter regular algebras. This construction generalizes the construction of Artin-Schelter regular Clifford algebras. 1991 Mathematics Subject Classification. 16W50, 14A22.
منابع مشابه
ar X iv : 1 50 2 . 06 01 5 v 1 [ m at h . R A ] 2 0 Fe b 20 15 m - KOSZUL ARTIN - SCHELTER REGULAR ALGEBRAS
This paper studies the homological determinants and Nakayama automorphisms of not-necessarily-noetherian m-Koszul twisted Calabi-Yau or, equivalently, m-Koszul Artin-Schelter regular, algebras. Dubois-Violette showed that such an algebra is isomorphic to a derivation quotient algebra D(w, i) for a unique-up-to-scalar-multiples twisted superpotential w. By definition, D(w, i) is the quotient of ...
متن کاملDouble Extension Regular Algebras
Abstract. We construct several families of Artin-Schelter regular algebras of global dimension four using double Ore extension and then prove that all these algebras are strongly noetherian, Auslander regular, Koszul and CohenMacaulay domains. Many regular algebras constructed in the paper are new and are not isomorphic to either a normal extension or an Ore extension of an Artin-Schelter regul...
متن کاملRegular Algebras of Dimension 4 and Their A∞-ext-algebras
We construct four families of Artin-Schelter regular algebras of global dimension four. This is a complete list of Artin-Schelter regular algebras of global dimension four that are generated by two elements of degree 1 and whose Ext-algebra satisfies certain “generic” conditions. These algebras are also strongly noetherian, Auslander regular and Cohen-Macaulay. One of the main tools is Keller’s...
متن کاملBinomial Skew Polynomial Rings, Artin-schelter Regularity, and Binomial Solutions of the Yang-baxter Equation
Let k be a field and X be a set of n elements. We introduce and study a class of quadratic k-algebras called quantum binomial algebras. Our main result shows that such an algebra A defines a solution of the classical Yang-Baxter equation (YBE), if and only if its Koszul dual A is Frobenius of dimension n, with a regular socle and for each x, y ∈ X an equality of the type xyy = αzzt, where α ∈ k...
متن کاملar X iv : 0 71 0 . 54 92 v 1 [ m at h . R A ] 2 9 O ct 2 00 7 Koszul Equivalences in A ∞ - Algebras
We prove a version of Koszul duality and the induced derived equivalence for Adams connected A∞-algebras that generalizes the classical Beilinson-Ginzburg-Soergel Koszul duality. As an immediate consequence, we give a version of the Bernšte˘ ın-Gel'fand-Gel'fand correspondence for Adams connected A∞-algebras. We give various applications. For example, a connected graded algebra A is Artin-Schel...
متن کامل