Related papers: Quantum Boolean Algebras
Boolean models are applied to deriving operator versions of the classical Farkas Lemma in the theory of simultaneous linear inequalities.
We announce a new approach to the octonions as quasiassociative algebras. We strip out the categorical and quasi-quantum group considerations of our longer paper and present here (without proof) some of the more algebraic conclusions
We discuss new problems in universal algebraic geometry and explain them by boolean equations.
Quantum Lie algebras are generalizations of Lie algebras which have the quantum parameter h built into their structure. They have been defined concretely as certain submodules of the quantized enveloping algebras. On them the quantum Lie…
For any finitely generated abelian group $Q$, we reduce the problem of classification of $Q$-graded simple Lie algebras over an algebraically closed field of "good" characteristic to the problem of classification of gradings on simple Lie…
Koszul algebras with quadratic Groebner bases, called strong Koszul algebras, are studied. We introduce affine algebraic varieties whose points are in one-to-one correspondence with certain strong Koszul algebras and we investigate the…
The quantum Frobenius map and it splitting are shown to descend to corresponding maps for generalized $q$-Schur algebras at a root of unity. We also define analogs of $q$-Schur algebras for any affine algebra, and prove the corresponding…
In mathematical aspect, we introduce quantum algorithm and the mathematical structure of quantum computer. Quantum algorithm is expressed by linear algebra on a finite dimensional complex inner product space. The mathematical formulations…
We propose a new definition of quantum metric spaces, or W*-metric spaces, in the setting of von Neumann algebras. Our definition effectively reduces to the classical notion in the atomic abelian case, has both concrete and intrinsic…
This is a survey of what is known and/or conjectured about the prime and primitive spectra of quantum algebras, of quantized coordinate rings in particular. The topological structure of these spectra, their relations to classical affine…
We study twisted modules for (weak) quantum vertex algebras and we give a conceptual construction of (weak) quantum vertex algebras and their twisted modules. As an application we construct and classify irreducible twisted modules for a…
A class of quantum analogues of compact symmetric spaces of classical type is introduced by means of constant solutions to the reflection equations. Their zonal spherical functions are discussed in connection with $q$-orthogonal…
After an historical introduction on the standard algebraic approach to quantum mechanics of large systems we review the basic mathematical aspects of the algebras of unbounded operators. After that we discuss in some details their relevance…
Boolean calculus has been studied extensively in the past in the context of switching circuits, error-correcting codes etc. This work generalizes several approaches to defining a differential calculus for Boolean functions. A unified theory…
We consider orthomodular posets endowed with a symmetric difference. We call them ODPs. Expressed in the quantum logic language, we consider quantum logics with an XOR-type connective. We study three classes of "almost Boolean" ODPs, two of…
We classify the centers of the quantized Weyl algebras that are PI and derive explicit formulas for the discriminants of these algebras over a general class of polynomial central subalgebras. Two different approaches to these formulas are…
Using von Neumann algebras, we extend the theory of quantum computation on a graph to a theory of computation on an arbitrary topological space.
The input and output algebras of an infinite qubit system and their representations are described.
Quantum algebraic observables representing localization in space-time of a Dirac electron are defined. Inertial motion of the electron is represented in the quantum algebra with electron mass acting as the generator of motion. Since…
In this paper, we consider the q-extensions of Boole polynomials. From those polynomials, we derive some new and interesting properties and identities related to special polynomials.