Right Coideal Subalgebras of the Quantum Borel Algebra of type G2

In this paper we describe the right coideal subalgebras containing all group-like elements of the multiparameter quantum group Uq+(g), where g is a simple Lie algebra of type G2, while the main parameter of quantization q is not a root of 1. If the multiplicative order t of q is finite, t>4, t different from 6, then the same classification remains valid for homogeneous right coideal subalgebras of the positive part uq+(g) of the multiparameter version of the small Lusztig quantum group

Verma and simple modules for quantum groups at non-abelian groups

The Drinfeld double D of the bosonization of a finite-dimensional Nichols algebra B(V) over a finite non-abelian group G is called a quantum group at a non-abelian group. We introduce Verma modules over such a quantum group D and prove that a Verma module has simple head and simple socle. This provides two bijective correspondences between the set of simple modules over D and the set of simple modules over the Drinfeld double D(G). As an example, we describe the lattice of submodules of the Verma modules over the quantum group at the symmetric group S3 attached to the 12-dimensional Fomin-Kirillov algebra, computing all the simple modules and calculating their dimensions.Comment: 29 pages, 4 figures v2: final version. Main changes: Theorem 5 is new and Sections 4.3, 4.4, 4.5 and 4.5 were improve

Representations of copointed Hopf algebras arising from the tetrahedron rack

We study the copointed Hopf algebras attached to the Nichols algebra of the affine rack \Aff(\F_4,\omega), also known as tetrahedron rack, and the 2-cocycle -1. We investigate the so-called Verma modules and classify all the simple modules. We conclude that these algebras are of wild representation type and not quasitriangular, also we analyze when these are spherical

On the representation theory of the Drinfeld Double of the Fomin-Kirillov Algebra FK 3

Let D be the Drinfeld double of FK3#S3 . We have described the simple D-modules in Pogorelsky and Vay (Adv. Math. 301, 423-457, 2016). In the present work, we describe the indecomposable summands of the tensor products between them. We classify the extensions of the simple modules and show that D is of wild representation type. We also investigate the projective modules and their tensor products.Fil: Pogorelsky, Barbara. Universidade Federal do Rio Grande do Sul; BrasilFil: Vay, Cristian Damian. Universidad Nacional de Córdoba; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentin

ILC Reference Design Report Volume 1 - Executive Summary

The International Linear Collider (ILC) is a 200-500 GeV center-of-mass high-luminosity linear electron-positron collider, based on 1.3 GHz superconducting radio-frequency (SCRF) accelerating cavities. The ILC has a total footprint of about 31 km and is designed for a peak luminosity of 2x10^34 cm^-2s^-1. This report is the Executive Summary (Volume I) of the four volume Reference Design Report. It gives an overview of the physics at the ILC, the accelerator design and value estimate, the detector concepts, and the next steps towards project realization.The International Linear Collider (ILC) is a 200-500 GeV center-of-mass high-luminosity linear electron-positron collider, based on 1.3 GHz superconducting radio-frequency (SCRF) accelerating cavities. The ILC has a total footprint of about 31 km and is designed for a peak luminosity of 2x10^34 cm^-2s^-1. This report is the Executive Summary (Volume I) of the four volume Reference Design Report. It gives an overview of the physics at the ILC, the accelerator design and value estimate, the detector concepts, and the next steps towards project realization