On the combinatorial rank of the quantum groups of type G2-Reference-Cited by-同舟云学术

On the combinatorial rank of the quantum groups of type G2

Published:2020-07-31 Issue:11 Volume:20 Page:
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

Dylewski Vanusa¹,Pogorelsky Barbara¹,Renz Carolina²

Affiliation:

1. Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves, 9500 Porto Alegre, RS, Brasil

2. Universidade Federal De Ciências da Saúde de Porto Alegre, Rua Sarmento Leite, 245 Porto Alegre, RS, Brasil

Abstract

In this paper, we calculate the combinatorial rank of the positive part [Formula: see text] of the multiparameter version of the small Lusztig quantum group, where [Formula: see text] is a simple Lie algebra of type [Formula: see text]. Supposing that the main parameter of quantization [Formula: see text] has multiplicative order [Formula: see text], where [Formula: see text] is finite, [Formula: see text], we prove that the combinatorial rank equals 3.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021949882150208X

Reference18 articles.

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

2. Nichols algebras with standard braiding

3. A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems

4. On the combinatorial rank of a graded braided bialgebra

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