We extend the Larson–Sweedler theorem [10] to weak Hopf algebras by proving that a finite dimensional weak bialgebra is a weak Hopf algebra iff it possesses a non-degenerate left integral. We show that the category of modules over a weak Hopf algebra is autonomous monoidal with semisimple unit and invertible modules. We also reveal the connection of invertible modules to left and right grouplik...

Background: Diabetic neuropathy is one of the major complications reported widely in type 2 diabetes. It affects all the sensory, autonomic and motor systems including auditory pathway. Objectives: Present study is focused on functional analysis of auditory pathway by Brainstem Auditory Evoked Response (BAER) and with Pure Tone Audiometry (PTA) in type 2 diabetes. To compare the same in healthy...

The moduli spaces of Yang-Mills connections on finitely generated projective modules associated with noncommutative flows are studied. It is actually shown that they are homeomorphic to those on dual modules associated with dual noncommutative flows. Moreover the method is also applicable to the case of noncommutative multi-flows.

This thesis concerns quantum cluster algebras. For skew-symmetric acyclic quantum cluster algebras, we express the quantum F -polynomials and the quantum cluster monomials in terms of Serre polynomials of quiver Grassmannians of rigid modules. Then we introduce a new family of graded quiver varieties together with a new t-deformation, and generalize Nakajima’s t-analogue of q-characters to thes...