ON REPRESENTATIONS OF QUANTUM GROUPS Uq(f(K, H)) To Prof. Yingbo Zhang on the occasion of her 60th birthday

ON REPRESENTATIONS OF QUANTUM GROUPS Uq(f(K,H))

An interesting class of algebras Uq(f(K, H)) were introduced and studied in [10] as further generalizations of another class of algebras Uq(f(K)) introduced in [11] (which are similar to Uq(sl2)). This new class of algebras include the Drinfeld double of the Borel subalgebra Uq(sl2) of the quantized enveloping algebra Uq(sl2) (or equivalently the two parameter quantum groups Ur,s(sl2) as studie...

Buckling of rectangular and hexagonal honeycomb under combined axial compression and transverse shear

Article history: Received 26 February 2013 Received in revised form 19 July 2013 Available online 17 August 2013 Dedicated to Prof. S. Kyriakides on the occasion of his 60th birthday.

On Representations of Quantum Groups

We construct families of irreducible representations for a class of quantum groups Uq(fm(K,H). First, we realize these quantum groups as Hyperbolic algebras. Such a realization yields natural families of irreducible weight representations for Uq(fm(K,H)). Second, we study the relationship between Uq(fm(K,H)) and Uq(fm(K)). As a result, any finite dimensional weight representation of Uq(fm(K,H))...

Completing the series of boron-nucleophilic cyanoborates: boryl anions of type NHC–B(CN)2 – † †Dedicated to Prof. Dr Evamarie Hey-Hawkins on the occasion of her 60th birthday. ‡ ‡Electronic supplementary information (ESI) available: Experimental procedures, full characterisation, crystallographic data and computational details. CCDC 1550754 (1B), 1550755 (2B), 1550760 (7B), 1550767 (K-8B), 1550769 (9), 1550740 (1C), 1550756 (2C), 1550774 (7C), 1550768 {[K(18-cr-6)]-8C}, 1550770 (11), 1550771 (13), 1550772 (14), 1550757 (3A), 1550759 (7A), 1550758 (4). For ESI and crystallographic data in CIF or other electronic format see DOI: 10.1039/c7sc02238g Click here for additional data file. Click here for additional data file.

CONSTRUCTING IRREDUCIBLE REPRESENTATIONS OF QUANTUM GROUPS Uq(f(K))

As generalizations of Uq(sl2), a class of algebras Uq(f(K)) were introduced and studied in [7]. For some special parameters f(K) = a(Km − K−m), a 6= 0, m ∈ N, Uq(f(K)) are Hopf algebras and hence quantum groups in the sense of Drinfeld ([3]). In this paper, we realize these algebras as Hyperbolic algebras ([12]). As an application of this realization, we obtain a natural construction of irreduc...