Exponentiations over the Quantum Algebra

Exponentiations over the universal enveloping algebra of sl2(C)

We construct, by model-theoretic methods, several exponentiations on the universal enveloping algebra U of the Lie algebra sl2(C). MSC: 16S30, 17B10, 03C60.

Hermitian metric on quantum spheres

The paper deal with non-commutative geometry. The notion of quantumspheres was introduced by podles. Here we define the quantum hermitianmetric on the quantum spaces and find it for the quantum spheres.

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

Primitivity of Permutation Groups, Coherent Algebras and Matrices

A coherent algebra is F-primitive if each of its non-identity basis matrices is primitive in the sense of Frobenius. We investigate the relationship between the primitivity of a permutation group, the primitivity of its centralizer algebra, and F-primitivity. The results obtained are applied to give new proofs of primitivity criteria for the exponentiations of permutation groups and of coherent...

Linear Algebra with Sub-linear Zero-Knowledge Arguments

We suggest practical sub-linear size zero-knowledge arguments for statements involving linear algebra. Given commitments to matrices over a finite field, we give a sub-linear size zero-knowledge argument that one committed matrix is the product of two other committed matrices. We also offer a sub-linear size zero-knowledge argument for a committed matrix being equal to the Hadamard product of t...