Abstract
Let k be an algebraically closed field, A a finite dimensional connected (p,q)-Koszul self-injective algebra with p,q≥2. In this paper, we prove that the Yoneda algebra of A is isomorphic to a twisted polynomial algebra A ![t;β] in one indeterminate t of degree q+1 in which A ! is the quadratic dual of A, β is an automorphism of A !, and t b = β(b)t for each t∈A !. As a corollary, we recover Theorem 5.3 of [2].
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bocklandt R, Schedler T and Wemyss M, Superpotentials and higher order derivations, J. Pure Appl. Algebra 214 (2010) 1501–1522
Brenner S, Butler M C R and King A D, Periodic algebras which are almost Koszul, Algebra Representation Theory 5 (2002) 331–367
Guo J Y, Coverings and truncations of graded self-injective algebrs, J. Algebra 355 (2012) 9–34
Martínez-Villa R, Graded, self-injective and Koszul Algebras, J. Algebra 215 (1999) 34–72
Wakamastu T, On graded Frobenius algebras, J. Algebra 267 (2003) 377–395
Yu X L, Almost Koszul algebras and stably Calabi-Yau algebras, J. Pure. Appl. Algebra 216 (2012) 337–354
Acknowledgements
This work is supported by Natural Science Foundation of China (#11271119 and #11201220) and by Hunan Provincial Innovation Foundation for Postgraduate (#CX2012B199).
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicating Editor: Parameswaran Sankaran
Rights and permissions
About this article
Cite this article
Lijing, Z. Yoneda algebras of almost Koszul algebras. Proc Math Sci 125, 477–485 (2015). https://doi.org/10.1007/s12044-015-0248-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12044-015-0248-1