相关论文: Quantum p-adic spaces and quantum p-adic groups

The paper is devoted to examples of non-commutative analytic spaces over valuation fields. Those include non-commutative affine spaces, quantum tori, K3 surfaces.

We present a short review of adelic quantum mechanics pointing out its non-Archimedean and noncommutative aspects. In particular, $p$-adic path integral and adelic quantum cosmology are considered. Some similarities between $p$-adic…

We introduce a class of non-commutative geometries, loosely referred to as para-spaces, which are manifolds equipped with sheaves of non-commutative algebras called para-algebras. A differential analysis on para-spaces is investigated,…

We consider a twisted version of quantum groups corepresentations. This generalization amounts to include in the theory the case where quantum space coordinates and its endomorphism matrix entries belong to a non-commutative quadratic…

Quantum groups and quantum homogeneous spaces - developed by several authors since the 80's - provide a large class of examples of algebras which for many reasons we interpret as `coordinate algebras' over noncommutative spaces. This…

We construct a family of quantum scalar fields over a $p-$adic spacetime which satisfy $p-$adic analogues of the G\aa rding--Wightman axioms. Most of the axioms can be formulated the same way in both, the Archimedean and non-Archimedean…

This is a brief review article of various applications of non-Archimedean geometry, p-adic numbers and adeles in modern mathematical physics.

We show the existence of group-theoretic sections of certain geometrically pro-nilpotent by abelian arithmetic fundamental groups of hyperbolic curves over p-adic local fields which are non-geometric, i.e., which do not arise from rational…

A motivation of using noncommutative and nonarchimedean geometry on very short distances is given. Besides some mathematical preliminaries, we give a short introduction in adelic quantum mechanics. We also recall to basic ideas and tools…

We consider selected aspects of (non-Archimedean) quantum mathematics and non-Archimedean (quantum) computation.

It is now a classical result that an algebraic space locally of finite type over $\mathbf{C}$ is analytifiable if and only if it is locally separated. In this paper we study non-archimedean analytifications of algebraic spaces. We construct…

Quantum groups lead to an algebraic structure that can be realized on quantum spaces. These are noncommutative spaces that inherit a well defined mathematical structure from the quantum group symmetry. In turn such quantum spaces can be…

Noncommutative Euclidean spaces -- otherwise known as Moyal spaces or quantum Euclidean spaces -- are a standard example of a non-compact noncommutative geometry. Recent progress in the harmonic analysis of these spaces gives us the…

The article is devoted to the investigation of properties of quasi-invariant measures with values in non-Archimedean fields such as: convolutions of measures and functions; continuity of functions of measures; non-associative noncommutative…

In this paper, we first introduce a quantum $n$-space with a cocommutative Hopf algebra structure. Then it is shown that to this quantum $n$-space there corresponds a derivation algebra of $\sigma$-twisted derivations related to some…

We survey commutative and non-commutative analogs of uniform algebras in the Archimedean settings and also offer some non-Archimedean examples. Constraints on the development of non-complex uniform algebras are also discussed.

We present a new non-Archimedean realization of the Fock representation of the q-oscillator algebras where the creation and annihilation operators act on complex-valued functions, which are defined on a non-Archimedean local field of…

Classical and quantum mechanics for an extended Heisenberg algebra with canonical commutation relations for position and momentum coordinates are considered. In this approach additional noncommutativity is removed from the algebra by linear…

In this investigation, we introduce the class of non-archimedean frames in spirit with the topological notion of non-archimedean spaces. We explore various properties of these frames - particularly their spaciality. We attach a base that…

A detailed study is made of the noncommutative geometry of $R^3_q$, the quantum space covariant under the quantum group $SO_q(3)$. For each of its two $SO_q(3)$-covariant differential calculi we find its metric, the corresponding frame and…