scholarly journals Construction of Finitely Presented Lie Algebras and Superalgebras

1996 ◽  
Vol 21 (3) ◽  
pp. 337-349 ◽  
Author(s):  
VLADIMIR P. GERDT ◽  
VLADIMIR V KORNYAK
Keyword(s):  
Lie Algebras ◽  
Finitely Presented

Intermediate growth in finitely presented algebras

2017 ◽  
Vol 27 (04) ◽  
pp. 391-401 ◽  
Author(s):  
Dilber Koçak
Keyword(s):  
Lie Algebras ◽  
Associative Algebras ◽  
Intermediate Growth ◽  
Type Formula ◽  
Growth Types ◽  
Finitely Presented

For any integer [Formula: see text], we construct examples of finitely presented associative algebras over a field of characteristic [Formula: see text] with intermediate growth of type [Formula: see text]. We produce these examples by computing the growth types of some finitely presented metabelian Lie algebras.

scholarly journals Finitely presented centre-by-metabelian Lie algebras

1999 ◽  
Vol 60 (2) ◽  
pp. 221-226 ◽  
Author(s):  
R.M. Bryant ◽  
J.R.J. Groves
Keyword(s):  
Lie Algebras ◽  
Finite Dimensional ◽  
Finitely Presented

It is shown that finitely presented centre-by-metabelian Lie algebras are Abelian-by-finite-dimensional.

scholarly journals Finite presentability of some metabelian Hopf algebras

2005 ◽  
Vol 72 (1) ◽  
pp. 109-127 ◽  
Author(s):  
Dessislava H. Kochloukova
Keyword(s):  
Abelian Group ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Hopf Algebras ◽  
Abelian Ideal ◽  
Finite Presentability ◽  
Finitely Presented ◽  
Homological Type

We classify the Hopf algebras U (L)#kQ of homological type FP2 where L is a Lie algebra and Q an Abelian group such that L has an Abelian ideal A invariant under the Q-action via conjugation and U (L/A)#kQ is commutative. This generalises the classification of finitely presented metabelian Lie algebras given by J. Groves and R. Bryant.

scholarly journals An algorithm for analysis of the structure of finitely presented Lie algebras

1997 ◽  
Vol Vol. 1 ◽  
Author(s):  
Vladimir P. Gerdt ◽  
Vladimir V. Kornyak
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Nonlinear Partial Differential Equations ◽  
Practical Importance ◽  
Physical Models ◽  
Generators And Relations ◽  
Defining Relations ◽  
Number Of Generators ◽  
Finite Set ◽  
Finitely Presented

International audience We consider the following problem: what is the most general Lie algebra satisfying a given set of Lie polynomial equations? The presentation of Lie algebras by a finite set of generators and defining relations is one of the most general mathematical and algorithmic schemes of their analysis. That problem is of great practical importance, covering applications ranging from mathematical physics to combinatorial algebra. Some particular applications are constructionof prolongation algebras in the Wahlquist-Estabrook method for integrability analysis of nonlinear partial differential equations and investigation of Lie algebras arising in different physical models. The finite presentations also indicate a way to q-quantize Lie algebras. To solve this problem, one should perform a large volume of algebraic transformations which is sharply increased with growth of the number of generators and relations. For this reason, in practice one needs to use a computer algebra tool. We describe here an algorithm for constructing the basis of a finitely presented Lie algebra and its commutator table, and its implementation in the C language. Some computer results illustrating our algorithmand its actual implementation are also presented.

Finitely presented metabelian restricted Lie algebras

2020 ◽  
Vol 560 ◽  
pp. 1107-1145
Author(s):  
Dessislava H. Kochloukova ◽  
Adriana Juzga León
Keyword(s):  
Lie Algebras ◽  
Restricted Lie Algebras ◽  
Finitely Presented

scholarly journals Some non-finitely presented Lie algebras

1998 ◽  
Vol 127 (2) ◽  
pp. 105-112 ◽  
Author(s):  
Joseph Abarbanel ◽  
Shmuel Rosset
Keyword(s):  
Lie Algebras ◽  
Finitely Presented
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