scholarly journals Symmetric pairs for Nichols algebras of diagonal type via star products

2020 ◽  
Vol 365 ◽  
pp. 107042
Author(s):  
Stefan Kolb ◽  
Milen Yakimov
Keyword(s):  
Star Products ◽  
Nichols Algebras

scholarly journals Bivariate continuous q-Hermite polynomials and deformed quantum Serre relations

2020 ◽  
pp. 2140016
Author(s):  
W. Riley Casper ◽  
Stefan Kolb ◽  
Milen Yakimov
Keyword(s):  
Recurrence Relations ◽  
Star Product ◽  
Hermite Polynomials ◽  
Star Products ◽  
Defining Relations ◽  
Algebraic Properties ◽  
Product Method ◽  
Usual Quantum ◽  
Multivariate Orthogonal Polynomials ◽  
Nichols Algebras

We introduce bivariate versions of the continuous [Formula: see text]-Hermite polynomials. We obtain algebraic properties for them (generating function, explicit expressions in terms of the univariate ones, backward difference equations and recurrence relations) and analytic properties (determining the orthogonality measure). We find a direct link between bivariate continuous [Formula: see text]-Hermite polynomials and the star product method of [S. Kolb and M. Yakimov, Symmetric pairs for Nichols algebras of diagonal type via star products, Adv. Math. 365 (2020), Article ID: 107042, 69 pp.] for quantum symmetric pairs to establish deformed quantum Serre relations for quasi-split quantum symmetric pairs of Kac–Moody type. We prove that these defining relations are obtained from the usual quantum Serre relations by replacing all monomials by multivariate orthogonal polynomials.

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 From VOAs to Short Star Products in SCFT

2021 ◽  
Vol 384 (1) ◽  
pp. 245-277
Author(s):  
Mykola Dedushenko
Keyword(s):  
Star Products

Value of High-Quality Logistics: Evidence from a Clash Between SF Express and Alibaba

2020 ◽  
Vol 66 (9) ◽  
pp. 3879-3902 ◽  
Author(s):  
Ruomeng Cui ◽  
Meng Li ◽  
Qiang Li
Keyword(s):  
Operations Management ◽  
Economic Value ◽  
Product Variety ◽  
Star Products ◽  
High Quality ◽  
Long Tail ◽  
Online Retail ◽  
Delivery Service ◽  
Product Delivery ◽  
Identification Strategy

Consumers regard product delivery as an important service component that influences their shopping decisions on online retail platforms. Delivering products to customers in a timely and reliable manner enhances customer experience and companies’ profitability. In this research, we explore the extent to which customers value a high-quality delivery experience when shopping online. Our identification strategy exploits a natural experiment: a clash between SF Express and Alibaba, the largest private logistics service provider with the highest reputation in delivery quality in China and the largest online retail platform in China, respectively. The clash resulted in Alibaba unexpectedly removing SF Express as a shipping option from Alibaba’s retail platform for 42 hours in June 2017. Using a difference-in-differences design, we analyze the market performance of 129,448 representative stock-keeping units on Alibaba to quantify the economic value of a high-quality delivery service to sales, product variety, and logistics rating. We find that the removal of the high-quality delivery option from Alibaba’s retail platform reduced sales by 14.56% during the clash, increased the contribution of long-tail to total sales—sales dispersion—by 3%, but did not impact the variety and logistics rating of sold products. Furthermore, we also identify product characteristics that attenuate the value of high-quality logistics and find that the removal of SF Express is more obstructive for (1) star products as compared with long-tail products because the same star products are likely to be supplied by competing retail platforms that customers can easily switch to, (2) expensive products because customers need a reliable delivery service to protect their valuable items from damage or loss, and (3) less-discounted products because customers are more willing to sacrifice the service quality over a price markdown. This paper was accepted by Victor Martínez-de-Albéniz, operations management.

scholarly journals Nichols algebras of group type with many quadratic relations

2011 ◽  
Vol 227 (5) ◽  
pp. 1956-1989 ◽  
Author(s):  
M. Graña ◽  
I. Heckenberger ◽  
L. Vendramin
Keyword(s):  
Group Type ◽  
Nichols Algebras

EXT ALGEBRA OF NICHOLS ALGEBRAS OF CARTAN TYPE A2

2013 ◽  
Vol 12 (04) ◽  
pp. 1250191
Author(s):  
XIAOLAN YU ◽  
YINHUO ZHANG
Keyword(s):  
Spectral Sequence ◽  
Hopf Algebras ◽  
Type A ◽  
Serre Spectral Sequence ◽  
Nichols Algebra ◽  
Cartan Type ◽  
Dynkin Diagrams ◽  
Full Structure ◽  
Pointed Hopf Algebras ◽  
Nichols Algebras

We give the full structure of the Ext algebra of any Nichols algebra of Cartan type A2 by using the Hochschild–Serre spectral sequence. As an application, we show that the pointed Hopf algebras [Formula: see text] with Dynkin diagrams of type A, D, or E, except for A1 and A1 × A1 with the order NJ > 2 for at least one component J, are wild.

scholarly journals On rigidity of Nichols algebras

2015 ◽  
Vol 219 (12) ◽  
pp. 5539-5559 ◽  
Author(s):  
Iván Angiono ◽  
Mikhail Kochetov ◽  
Mitja Mastnak
Keyword(s):  
Nichols Algebras
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