A finite-dimensional Lie algebra arising from a Nichols algebra of diagonal type (rank 2)

被引：5

作者：

Andruskiewitsch, Nicolas ^{[1
]}

Angiono, Ivan ^{[1
]}

Rossi Bertone, Fiorela ^{[1
]}

机构：

[1] Univ Nacl Cordoba, CONICET, FaMAF CIEM, Medina Allende S-N,Ciudad Univ, RA-5000 Cordoba, Argentina

来源：

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN | 2017年 / 24卷 / 01期

关键词：

QUANTUM GROUPS;

D O I：

10.36045/bbms/1489888813

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let B-q be a finite-dimensional Nichols algebra of diagonal type corresponding to a matrix q is an element of k (theta x theta). Let L-q be the Lusztig algebra associated to B-q [AAR]. We present L-q as an extension (as braided Hopf algebras) of B-q by 3q where 3(q) is isomorphic to the universal enveloping algebra of a Lie algebra n(q). We compute the Lie algebra nq when theta = 2.

引用

页码：15 / 34

页数：20

共 50 条

[1] The quantum divided power algebra of a finite-dimensional Nichols algebra of diagonal type
Andruskiewitsch, Nicolas
Angiono, Ivan
Rossi Bertone, Fiorela
[J]. MATHEMATICAL RESEARCH LETTERS, 2017, 24 (03) : 619 - 643
[2] Examples of finite-dimensional rank 2 Nichols algebras of diagonal type
Heckenberger, I.
[J]. COMPOSITIO MATHEMATICA, 2007, 143 (01) : 165 - 190
[3] The Heisenberg envelope for the Hochschild algebra of a finite-dimensional lie algebra
Razmyslov Y.P.
Pogudin G.A.
[J]. Journal of Mathematical Sciences, 2013, 193 (4) : 580 - 585
[4] Rank 4 finite-dimensional Nichols algebras of diagonal type in positive characteristic
Wang, Jing
[J]. JOURNAL OF ALGEBRA, 2020, 559 : 547 - 579
[5] Finite-dimensional Lie subalgebras of the Weyl algebra
de Traubenberg, Michel Rausch
Slupinski, Marcus J.
Tanasa, Adrian
[J]. JOURNAL OF LIE THEORY, 2006, 16 (03) : 427 - 454
[6] How abelian is a finite-dimensional Lie algebra?
Riley, DM
[J]. FORUM MATHEMATICUM, 2003, 15 (03) : 455 - 463
[7] On the Exterior Degree of a Finite-Dimensional Lie Algebra
Shamsaki, Afsaneh
Parvizi, Mohsen
Erfanian, Ahmad
[J]. JOURNAL OF MATHEMATICS, 2024, 2024
[8] ON THE LIE ALGEBRA STRUCTURE OF HH1 (A) OF A FINITE-DIMENSIONAL ALGEBRA A
Linckelmann, Markus
Degrassi, Lleonard Rubio Y.
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2020, 148 (05) : 1879 - 1890
[9] CONTINUOUS FAMILY OF FINITE-DIMENSIONAL REPRESENTATIONS OF A SOLVABLE LIE-ALGEBRA ARISING FROM SINGULARITIES
YAU, SST
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA-PHYSICAL SCIENCES, 1983, 80 (24): : 7694 - 7696
[10] On the sum of an almost abelian lie algebra and a lie algebra finite-dimensional over its center
Petravchuk A.P.
[J]. Ukrainian Mathematical Journal, 1999, 51 (5) : 707 - 715

← 1 2 3 4 5 →