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Title:A relation between quasi-twisted codes and2-D constacyclic codes
Abstract:Quasi-twisted codes are generalizations of the familiar linear quasi-cyclic codes.In thistalk, we apply an algebraic method to investigate the relationshipbetween quasi-twisted codes constacyclic codes. Moreover, a generator polynomial of a quasi-twisted code with constacyclic constituent codes is given.Meanwhile, we obtain the necessary conditions for a quasi-twisted code C ofindex ‘ and length ‘m to be equivalent to a constacyclic code of length ‘m.Finally, some examples are presented to illustrate the discussed results.
Title:Noncommutative matrix factorization and quadric surfaces
Abstract:In this talk, I will briefly introduce recent progress in the theory of noncommutative matrix factorations of normal regular elements in Artin-Schelter regular algebras. In particular, I will focus on noncommutative quadrics which are related to Clifford deformations of Koszul Frobenius algebras.
Title:Trunction of unitary operads
Abstract:In this talk, we will introduce the truncation ideals of a k-linear
unitary symmetric operad and use them to study ideals structure, growth
property and to classify operads of low Gelfand-Kirillow dimension. This work
is joint with Yu Ye and James J. Zhang.
Title: Some homological invariant properties under Frobenius extensions
Abstract:Frobenius extensionswere firstlyintroduced by Kasch as a generalizationof Frobenius algebra. In this talk, we will show that, for a Frobenius extension, a module over the extensionring is Gorenstein projective if and only if so is its underlying module overthe base ring.For a separable Frobenius extensionbetween Artin algebras, we obtain thatsome homological properties are invariant, including CM-finiteness, CM-freeness and the representation dimension of Artin alebra.