scholarly journals Enveloping algebras with just infinite Gelfand–Kirillov dimension

2020 ◽  
Vol 58 (2) ◽  
pp. 285-306
Author(s):  
Natalia K. Iyudu ◽  
Susan J. Sierra
Keyword(s):  
Enveloping Algebras ◽  
Kirillov Dimension

Universal Enveloping Algebras of Simple Symplectic Anti-Jordan Triple Systems

2015 ◽  
Vol 22 (02) ◽  
pp. 281-292 ◽  
Author(s):  
Marina Tvalavadze
Keyword(s):  
Associative Algebra ◽  
Triple System ◽  
Universal Enveloping Algebras ◽  
Triple Systems ◽  
Enveloping Algebras ◽  
Injective Homomorphism ◽  
Pbw Basis ◽  
Finite Dimensional ◽  
Jordan Triple Systems ◽  
Kirillov Dimension

In this work we are concerned with the universal associative envelope of a finite-dimensional simple symplectic anti-Jordan triple system (AJTS). We prove that if 𝕋 is a triple system as above, then there exists an associative algebra U(𝕋) and an injective homomorphism ε : 𝕋 → U(𝕋), where U(𝕋) is an AJTS under the triple product defined by (a,b,c) = abc - cba. Moreover, U(𝕋) is a universal object with respect to such homomorphisms. We explicitly determine the PBW-basis of U(𝕋), the center Z(U(𝕋)) and the Gelfand-Kirillov dimension of U(𝕋).

scholarly journals On S-Evolution Algebras and Their Enveloping Algebras

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1195
Author(s):  
Farrukh Mukhamedov ◽  
Izzat Qaralleh
Keyword(s):  
Enveloping Algebras

In the present paper, we introduce S-evolution algebras and investigate their solvability, simplicity, and semisimplicity. The structure of enveloping algebras has been carried out through the attached graph of S-evolution algebras. Moreover, we introduce the concept of E-linear derivation of S-evolution algebras, and prove such derivations can be extended to their enveloping algebras under certain conditions.

scholarly journals EXAMPLES OF FINITE-DIMENSIONAL POINTED HOPF ALGEBRAS IN CHARACTERISTIC 2

2020 ◽  
pp. 1-14
Author(s):  
NICOLÁS ANDRUSKIEWITSCH ◽  
DIRCEU BAGIO ◽  
SARADIA DELLA FLORA ◽  
DAIANA FLÔRES
Keyword(s):  
Hopf Algebras ◽  
Abelian Groups ◽  
Vector Spaces ◽  
Group Algebras ◽  
Finite Abelian Groups ◽  
Finite Dimensional ◽  
Pointed Hopf Algebras ◽  
Characteristic 2 ◽  
Nichols Algebras ◽  
Kirillov Dimension

Abstract We present new examples of finite-dimensional Nichols algebras over fields of characteristic 2 from braided vector spaces that are not of diagonal type, admit realizations as Yetter–Drinfeld modules over finite abelian groups, and are analogous to Nichols algebras of finite Gelfand–Kirillov dimension in characteristic 0. New finite-dimensional pointed Hopf algebras over fields of characteristic 2 are obtained by bosonization with group algebras of suitable finite abelian groups.

scholarly journals Quantun function algebras as quantum enveloping algebras

1998 ◽  
Vol 26 (6) ◽  
pp. 1795-1818 ◽  
Author(s):  
Fabio Gavarini
Keyword(s):  
Enveloping Algebras ◽  
Function Algebras

scholarly journals Fox-type problems in enveloping algebras

2008 ◽  
Vol 319 (6) ◽  
pp. 2489-2495 ◽  
Author(s):  
Hamid Usefi
Keyword(s):  
Enveloping Algebras

scholarly journals Gelfand-Kirillov Dimensions of Modules over Differential Difference Algebras

2016 ◽  
Vol 23 (04) ◽  
pp. 701-720 ◽  
Author(s):  
Xiangui Zhao ◽  
Yang Zhang
Keyword(s):  
Computational Method ◽  
Finitely Generated ◽  
Finitely Generated Module ◽  
Polynomial Algebras ◽  
Ore Extensions ◽  
Basis Method ◽  
Finitely Generated Modules ◽  
Kirillov Dimension

Differential difference algebras are generalizations of polynomial algebras, quantum planes, and Ore extensions of automorphism type and of derivation type. In this paper, we investigate the Gelfand-Kirillov dimension of a finitely generated module over a differential difference algebra through a computational method: Gröbner-Shirshov basis method. We develop the Gröbner-Shirshov basis theory of differential difference algebras, and of finitely generated modules over differential difference algebras, respectively. Then, via Gröbner-Shirshov bases, we give algorithms for computing the Gelfand-Kirillov dimensions of cyclic modules and finitely generated modules over differential difference algebras.

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