supported by ZJNSF(LY19A010011);NSFC(11971141,12371017);supported by NSFC(11971449,12131015,12371042).
A Clifford deformation of a Koszul Frobenius algebra E is a finite dimensional Z_(2)-graded algebra E(θ),which corresponds to a noncommutative quadric hypersurface E^(!)/(z)for some central regular element z∈E_(2)^(...
Natural Science Foundation of Gansu Province(22JR11RA138,20JR5RA249);National Natural Science Foundation of China(12071191);Funds for Innovative Fundamental Research Group Project of Gansu Province(23JRRA684)。
Let A be a path A∞-algebra over a positively graded quiver Q. We prove that the derived category of A is triangulated equivalent to the derived category of kQ, which is viewed as a DG algebra with trivial differentia...
The author is very grateful to the referees for helpful comments. He thanks Professor Yu Ye for numerous discussion and suggestions. This work was supported in part by the National Natural Science Foundation of China (Grant No. 11471017), Doctoral Research Foundation, and the Research Culture Foundation of Anhui Normal University (No. 2014xmpyll).
Let A be a Koszul algebra, and let M be a graded A-bimodule. We prove that the trivial extension algebra of A by M is also a Koszul algebra whenever M is Koszul as a left A-module. Applications and examples are also p...
The first author is and encouragement. The authors thank grateful to Professor Yu Ye for helpful discussion the anonymous referees for their very helpful suggestions to improve this paper. This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11571341, 11371186).
Let A and B be algebras, and let T be the dual extension algebra of A and B. We provide a different method to prove that T is Koszul if and only if both A and B are Koszul. Furthermore, we prove that an algebra is Kos...
This work was supported by the National Natural Science Foundation of China (Grant Nos. 11571316, 11001245) and the Natural Science Foundation of Zhejiang Province (Grant No. LY16A010003).
Given any integers a,b,c, and d with a 〉 1, c ≥ 0, b ≥ a+c, and d ≥ b + c, the notion of (a, b, c, d)-Koszul algebra is introduced, which is another class of standard graded algebras with "nonpure" resolutio...