scholarly journals Gröbner bases of associative algebras and the Hochschild cohomology

2004 ◽  
Vol 357 (3) ◽  
pp. 1095-1124 ◽  
Author(s):  
Yuji Kobayashi
Keyword(s):  
Hochschild Cohomology ◽  
Gröbner Bases ◽  
Grobner Bases ◽  
Associative Algebras

scholarly journals Distributive laws between the operads Lie and Com

2020 ◽  
Vol 30 (08) ◽  
pp. 1565-1576
Author(s):  
Murray Bremner ◽  
Vladimir Dotsenko
Keyword(s):  
Lie Algebras ◽  
Computer Algebra ◽  
Gröbner Bases ◽  
Classification Problem ◽  
Grobner Bases ◽  
Polynomial Rings ◽  
Associative Algebras ◽  
Distributive Law ◽  
Free Modules

Using methods of computer algebra, especially, Gröbner bases for submodules of free modules over polynomial rings, we solve a classification problem in theory of algebraic operads: we show that the only nontrivial (possibly inhomogeneous) distributive law between the operad of Lie algebras and the operad of commutative associative algebras is given by the Livernet–Loday formula deforming the Poisson operad into the associative operad.

Synergy in the Theories of Gröbner Bases and Path Algebras

1993 ◽  
Vol 45 (4) ◽  
pp. 727-739 ◽  
Author(s):  
Daniel R. Farkas ◽  
C. D. Feustel ◽  
Edward L. Green
Keyword(s):  
General Theory ◽  
Gröbner Basis ◽  
Gröbner Bases ◽  
Grobner Bases ◽  
Polynomial Rings ◽  
Grobner Basis ◽  
Associative Algebras ◽  
Path Algebras

AbstractA general theory for Grôbner basis in path algebras is introduced which extends the known theory for commutative polynomial rings and free associative algebras.

scholarly journals Gröbner bases for operads

2010 ◽  
Vol 153 (2) ◽  
pp. 363-396 ◽  
Author(s):  
Vladimir Dotsenko ◽  
Anton Khoroshkin
Keyword(s):  
Gröbner Bases ◽  
Grobner Bases
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