Input
Quiver Qchoose input format
Draw quiver Qvertices 0, arrows 0
Path composition from left to right
Output
Reduced Gröbner basis G and W = Tip(G)
Quiver Q
Ufnarovski graph QW
Anick chains W(n)
Morse zigzag differential
Hochschild cohomology HHn(A)
Cohomology basis on demand
HH computation log
Click Show degrees, then choose a degree to compute Hochschild cohomology or homology.
Hochschild homology HHn(A)
Homology basis on demand
HH computation log
Click Show degrees, then choose a degree to compute Hochschild cohomology or homology.
Computation Data
Messages
References
Main reference
[CLZ] J. Chen, Y. Liu, and G. Zhou, Algebraic Morse theory via homological perturbation lemma, arXiv:2404.10165, 2025.
Related references
[Bar] M. J. Bardzell, The alternating syzygy behavior of monomial algebras, J. Algebra, vol. 188, no. 1, pp. 69-89, 1997.
[CS] S. Chouhy and A. Solotar, Projective resolutions of associative algebras and ambiguities, J. Algebra, vol. 432, pp. 22-61, 2015.
[Ger] M. Gerstenhaber, The cohomology structure of an associative ring, Ann. Math., vol. 78, no. 2, pp. 267-288, 1963.
[Gre] E. L. Green, Noncommutative Gröbner bases, and projective resolutions, in Computational Methods for Representations of Groups and Algebras: Euroconference in Essen (Germany), Basel: Birkhäuser Basel, 1999, pp. 29-60.