Gröbner–Shirshov Bases for Replicated Algebras Full article
| Journal |
Algebra Colloquium
ISSN: 1005-3867 |
||
|---|---|---|---|
| Output data | Year: 2017, Volume: 24, Number: 04, Pages: 563-576 Pages count : 14 DOI: 10.1142/s1005386717000372 | ||
| Tags | di-algebra; Gröbner-Shirshov basis; tri-algebra | ||
| Authors |
|
||
| Affiliations |
|
Abstract:
We establish a universal approach to solutions of the word problem in the varieties of di- and tri-algebras. This approach, for example, allows us to apply Gröbner–Shirshov bases method for Lie algebras to solve the ideal membership problem in free Leibniz algebras (Lie di-algebras). As another application, we prove an analogue of the Poincaré–Birkhoff–Witt Theorem for universal enveloping associative tri-algebra of a Lie tri-algebra (CTD!-algebra).
Cite:
Kolesnikov P.S.
Gröbner–Shirshov Bases for Replicated Algebras
Algebra Colloquium. 2017. V.24. N04. P.563-576. DOI: 10.1142/s1005386717000372 WOS Scopus OpenAlex
Gröbner–Shirshov Bases for Replicated Algebras
Algebra Colloquium. 2017. V.24. N04. P.563-576. DOI: 10.1142/s1005386717000372 WOS Scopus OpenAlex
Dates:
| Submitted: | Jan 2, 2017 |
Identifiers:
| Web of science: | WOS:000415364500003 |
| Scopus: | 2-s2.0-85034055887 |
| OpenAlex: | W2656423269 |