Universal Algebra Applied to Hom-Associative Algebras, and More

被引：8

作者：

Hellstrom, Lars ^{[1
]}

Makhlouf, Abdenacer ^{[2
]}

Silvestrov, Sergei D. ^{[1
]}

机构：

[1] Malardalen Univ, Sch Educ Culture & Commun, Div Appl Math, Box 883, S-72123 Vasteras, Sweden

[2] Univ Haute Alsace, LMIA, F-68093 Mulhouse, France

来源：

ALGEBRA, GEOMETRY AND MATHEMATICAL PHYSICS (AGMP) | 2014年 / 85卷

基金：

瑞典研究理事会;

关键词：

VIRASORO ALGEBRA; LIE-ALGEBRAS; DEFORMATIONS;

D O I：

10.1007/978-3-642-55361-5_11

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this paper is to discuss the universal algebra theory of hom-algebras. This kind of algebra involves a linear map which twists the usual identities. We focus on hom-associative algebras and hom-Lie algebras for which we review the main results. We discuss the envelopment problem, operads, and the Diamond Lemma; the usual tools have to be adapted to this new situation. Moreover we study Hilbert series for the hom-associative operad and free algebra, and describe them up to total degree equal 8 and 9 respectively.

引用

页码：157 / 199

页数：43

共 51 条

[1] Q-DEFORMATION OF THE VIRASORO ALGEBRA WITH CENTRAL EXTENSION [J].

AIZAWA, N ;

SATO, H .

PHYSICS LETTERS B, 1991, 256 (02) :185-190

[2]

Ammar F, 2011, J LIE THEORY, V21, P813

[3] Horn-Lie superalgebras and Horn-Lie admissible superalgebras [J].

Ammar, Faouzi ;

Makhlouf, Abdenacer .

JOURNAL OF ALGEBRA, 2010, 324 (07) :1513-1528

[4]

[Anonymous], 1965, Universal Algebra

[5] Generalization of n-ary Nambu algebras and beyond [J].

Ataguema, H. ;

Makhlouf, A. ;

Silvestrov, S. .

JOURNAL OF MATHEMATICAL PHYSICS, 2009, 50 (08)

[6] Hom-Lie algebras with symmetric invariant nondegenerate bilinear forms [J].

Benayadi, Said ;

Makhlouf, Abdenacer .

JOURNAL OF GEOMETRY AND PHYSICS, 2014, 76 :38-60

[7] MONOIDAL HOM-HOPF ALGEBRAS [J].

Caenepeel, S. ;

Goyvaerts, I. .

COMMUNICATIONS IN ALGEBRA, 2011, 39 (06) :2216-2240

[8] Q-DEFORMATIONS OF VIRASORO ALGEBRA AND CONFORMAL DIMENSIONS [J].

CHAICHIAN, M ;

ISAEV, AP ;

LUKIERSKI, J ;

POPOWICZ, Z ;

PRESNAJDER, P .

PHYSICS LETTERS B, 1991, 262 (01) :32-38

[9] Q-VIRASORO ALGEBRA AND ITS RELATION TO THE Q-DEFORMED KDV SYSTEM [J].

CHAICHIAN, M ;

POPOWICZ, Z ;

PRESNAJDER, P .

PHYSICS LETTERS B, 1990, 249 (01) :63-65

[10] QUANTUM CONFORMAL ALGEBRA WITH CENTRAL EXTENSION [J].

CHAICHIAN, M ;

ELLINAS, D ;

POPOWICZ, Z .

PHYSICS LETTERS B, 1990, 248 (1-2) :95-99

← 1 2 3 4 5 6 →