A(infinity)-algebra structures associated to K-2 algebras

作者：Conner Andrew^*; Goetz Pete

来源：Journal of Algebra, 2011, 337(1): 63-81.

DOI：10.1016/j.jalgebra.2011.04.031

• K-2 algebras
• A(infinity)-algebras
• Yoneda algebra

The notion of a K-2-algebra was recently introduced by Cassidy and Shelton as a generalization of the notion of a Koszul algebra. The Yoneda algebra of any connected graded algebra admits a canonical A(infinity)-algebra structure. This structure is trivial if the algebra is Koszul. We study the A(infinity)-structure on the Yoneda algebra of a K-2-algebra. For each non-negative integer n we prove the existence of a K-2-algebra B and a canonical A(infinity)-algebra structure on the Yoneda algebra of B such that the higher multiplications m(i) are nonzero for all 3 <= i <= n + 3. We also provide examples which show that the K-2 property is not detected by any obvious vanishing patterns among higher multiplications.

• 出版日期2011-7-1