WebAzam, H. Yamane and M. Yousofzadeh , Classification of finite-dimensional irreducible representations of generalized quantum groups via Weyl groupoids, Publ. Res. Inst. Math. Sci. 51(1) ... Weyl groupoids with at most three objects, J. … WebJan 15, 2012 · Using the classification of finite Weyl groupoids we prove that crystallographic arrangements, a large subclass of the class of simplicial arrangements which was recently defined, are hereditarily inductively free. In particular, all crystallographic reflection arrangements are hereditarily inductively free, among them the arrangement of …
Root systems and Weyl groupoids for Nichols algebras
WebMay 27, 2015 · Over fields of arbitrary characteristic we classify all rank three Nichols algebras of diagonal type with a finite root system. Our proof uses the classification of the finite Weyl groupoids of rank three. Giving Week! Show your support for Open Science by donating to arXiv during Giving Week, April 25th-29th. DONATE. WebThe result is a correspondence between Weyl groupoids permitting a root system and Tits arrangements satisfying an integrality condition which we call the crystallographic property. Abstract We translate the axioms of a Weyl groupoid with (not necessarily finite) root system in terms of arrangements. The result is a correspondence between Weyl ... statement of information efile
Finite Group -- from Wolfram MathWorld
WebMay 15, 2024 · Weyl groupoids have successfully been used as a tool in classifications, see for example [16]. Motivated by these algebras, Heckenberger and the author classified the finite Weyl groupoids and thus a subclass of the class of simplicial arrangements, the so called crystallographic arrangements ([10]). WebApr 23, 2024 · In Lie theory, a Weyl group is a group associated with a compact Lie group that can either be abstractly defined in terms of a root system or in terms of a maximal … WebJan 15, 2009 · In the present paper arithmetic root systems are classified in full generality. As a byproduct many new finite dimensional pointed Hopf algebras are obtained. Previous article in issue; Next article in issue; MSC. 17B37. 16W35. Keywords. Hopf algebra. Nichols algebra. Weyl groupoid. Advances in Mathematics 220 (2009) 59–124 www.elsevier ... statement of inheritance tdhca