8 citations · 56 across the 16 of their papers we have counts for
18 papers
Spectral gaps for twisted Dolbeault-Dirac operators over the irreducible quantum flag manifolds
Biswarup Das, Réamonn Ó Buachalla, Petr Somberg
We show that tensoring the Laplace and Dolbeault-Dirac operators of a Kähler structure (with closed integral) by a negative Hermitian holomorphic module, produces operators with sp…
Second cohomology groups of the Hopf-algebras associated to universal unitary quantum groups
Biswarup Das, Uwe Franz, Anna Kula +1
We compute the second (and the first) cohomology groups of -algebras associated to the universal quantum unitary groups of not neccesarily Kac type, extending our earlier resul…
The RFD and KAC quotients of the Hopf*-algebras of universal orthogonal quantum groups
Biswarup Das, Uwe Franz, Adam Skalski
We determine the Kac quotient and the RFD (residually finite dimensional) quotient for the Hopf *-algebras associated to universal orthogonal quantum groups.
Quadratic number of nodes is sufficient to learn a dataset via gradient descent
Biswarup Das, Eugene. A. Golikov
We prove that if an activation function satisfies some mild conditions and number of neurons in a two-layered fully connected neural network with this activation function is beyond…
Compact Quantum Homogeneous Kähler Spaces
Biswarup Das, Réamonn Ó Buachalla, Petr Somberg
Noncommutative Kähler structures were recently introduced as an algebraic framework for studying noncommutative complex geometry on quantum homogeneous spaces. In this paper, we in…
A Dolbeault-Dirac Spectral Triple for Quantum Projective Space
Biswarup Das, Réamonn Ó Buachalla, Petr Somberg
The notion of a Kähler structure for a differential calculus was recently introduced by the second author as a framework in which to study the noncommutative geometry of the quantu…
Invariant Markov semigroups on quantum homogeneous spaces
Biswarup Das, Uwe Franz, Xumin Wang
Invariance properties of linear functionals and linear maps on algebras of functions on quantum homogeneous spaces are studied, in particular for the special case of expected coide…
Admissibility Conjecture and Kazhdan's Property (T) for quantum groups
Biswarup Das, Matthew Daws, Pekka Salmi
We give a partial solution to a long-standing open problem in the theory of quantum groups, namely we prove that all finite-dimensional representations of a wide class of locally c…
Lévy-Khintchine decompositions for generating functionals on algebras associated to universal compact quantum groups
Biswarup Das, Uwe Franz, Anna Kula +1
We study the first and second cohomology groups of the -algebras of the universal unitary and orthogonal quantum groups and . This provides valuable information…
On a quantum version of Ellis joint continuity theorem
Biswarup Das, Colin Mrozinski
We give a necessary and sufficient condition on a compact semitopological quantum semigroup which turns it into a compact quantum group. In particular, we obtain a generalisation o…
One-to-one correspondence between generating functionals and cocycles on quantum groups in presence of symmetry
Biswarup Das, Uwe Franz, Anna Kula +1
We prove that under a symmetry assumption all cocycles on Hopf *-algebras arise from generating functionals. This extends earlier results of R.Vergnioux and D.Kyed and has two quan…
Quantum Eberlein compactifications and invariant means
Biswarup Das, Matthew Daws
We propose a definition of a "-Eberlein" algebra, which is a weak form of a -bialgebra with a sort of "unitary generator". Our definition is motivated to ensure that comm…
Rigidity of action of compact quantum groups III: the general case
Debashish Goswami
If a compact quantum group acts faithfully and smoothly (in the sense of Goswami 2009) on a smooth, compact, oriented, connected Riemannian manifold such that the action induces a…
Rigidity of action of compact quantum groups II
Biswarup Das, Debashish Goswami, Soumalya Joardar
Suppose that a compact quantum group Q acts faithfully and isomet- rically (in the sense of [10]) on a smooth compact, oriented, connected Riemannian manifold M . If the manifold i…
Quantum gauge symmetries in Noncommutative Geometry
Jyotishman Bhowmick, Francesco D'Andrea, Biswarup Das +1
We discuss generalizations of the notion of i) the group of unitary elements of a (real or complex) finite dimensional C*-algebra, ii) gauge transformations and iii) (real) automor…
Quantum Brownian Motion on noncommutative manifolds: construction, deformation and exit times
Biswarup Das, Debashish Goswami
We begin with a review and analytical construction of quantum Gaussian process (and quantum Brownian motions) in the sense of [25],[10] and others, and then formulate and study in…
Dilation of arbitrary symmetric quantum dynamical semigroups on $B(\clh)$
Biswarup Das
We prove the existence of Hudson Parthasarathy dilation of a quantum dynamical semigroup on $B(\clh),$ which is symmetric with respect to the canonical normal trace on it.
A homomorphism theorem and a Trotter product formula for quantum stochastic flows with unbounded coefficients
Biswarup Das, Debashish Goswami, Kalyan B. Sinha
We give a new method for proving the homomorphic property of a quantum stochastic ow satisfying a quantum stochastic differential equation with unbounded coefficients, under some f…