Related papers: Differential calculus on quantum groups: Construct…
We develop a general theory of `quantum' diffeomorphism groups based on the universal comeasuring quantum group $M(A)$ associated to an algebra $A$ and its various quotients. Explicit formulae are introduced for this construction, as well…
For transcendental values of q the quantum tangent spaces of all left-covariant first order differential calculi of dimension less than four on the quantum group $\SLq 2$ are given. All such differential calculi $\Gamma $ are determined and…
Intrinsic Hopf algebra structure of the Woronowicz differential complex is shown to generate quite naturally a bicovariant algebra of four basic objects within a differential calculus on quantum groups -- coordinate functions, differential…
We study equivariant birationality from the perspective of derived categories. We produce examples of nonlinearizable but stably linearizable actions of finite groups on smooth cubic fourfolds.
We provide the Cartan calculus for bicovariant differential forms on bicrossproduct quantum groups $k(M)\lrbicross kG$ associated to finite group factorizations $X=GM$ and a field $k$. The irreducible calculi are associated to certain…
We construct a two-parameter covariant differential calculus on the quantum $h$-exterior plane. We also give a deformation of the two-dimensional fermionic phase space.
A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced…
We construct compact parametrix implementations of covariant derivations on the quantum annulus.
By working with several specific Poisson-Lie groups arising from Heisenberg Lie bialgebras and by carrying out their quantizations, a case is made for a useful but simple method of constructing locally compact quantum groups. The strategy…
Canonical differential calculus is defined for finitely generated abelian group with an involution existing consistently. Two such canonical calculi are found out. Fermionic representation for canonical calculus is defined based on…
We consider two different types of deformations for the linear group $ GL(n)$ which correspond to using of a general diagonal R-matrix. Relations between braided and quantum deformed algebras and their coactions on a quantum plane are…
This research paper gives an overview of quantum computers - description of their operation, differences between quantum and silicon computers, major construction problems of a quantum computer and many other basic aspects. No special…
We develop a construction of the unitary type anti-involution for the quantized differential calculus over $GL_q(n)$ in the case $|q|=1$. To this end, we consider a joint associative algebra of quantized functions, differential forms and…
The Poisson structures on two-dimensional Galilei group, classified in the author previous paper are quantized. The dual quantum Galilei Lie algebras are found.
The quantum Galilei group $G_{\varkappa}$ is defined. The bicrossproduct structure of $G_{\varkappa}$ and the corresponding Lie algebra is revealed. The projective representations for the two-dimensional quantum Galilei group are…
We consider GLq(N)-covariant quantum algebras with generators satisfying quadratic polynomial relations. We show that, up to some inessential arbitrariness, there are only two kinds of such quantum algebras, namely, the algebras with…
The central structure in various versions of noncommutative geometry is a differential calculus on an associative algebra. This is an analogue of the calculus of differential forms on a manifold. In this short review we collect examples of…
Classical mechanics can be formulated using a symplectic structure on classical phase space, while quantum mechanics requires a complex-differentiable structure on that same space. Complex-differentiable structures on a given real manifold…
In this review article the construction of first order coordinate differential calculi on finitely generated and finitely related associative algebras are considered and explicit construction of the bimodule of one form over such algebras…
We associate to any (suitable) bicovariant differential calculus on a quantum group a Cartan Hopf algebra which has a left, respectively right, representation in terms of left, respectively right, Cartan calculus operators. The example of…