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Filtered Lie conformal algebras whose associated graded algebras are isomorphic to that of general conformal algebra $gc_1$
Lie conformal algebras filtered algebras general conformal algebras second cohomology groups
2011/8/25
Abstract: Let $G$ be a filtered Lie conformal algebra whose associated graded conformal algebra is isomorphic to that of general conformal algebra $gc_1$. In this paper, we prove that $G\cong gc_1$ or...
Notes on Ding-Iohara algebra and AGT conjecture
Ding-Iohara algebra AGT conjecture High Energy Physics Theory
2011/7/26
Notes on Ding-Iohara algebra and AGT conjecture.
Noncommutative spectral geometry, algebra doubling and the seeds of quantization
Noncommutative spectral geometry algebra doubling the seeds of quantization
2011/7/26
Abstract: A physical interpretation of the two-sheeted space, the most fundamental ingredient of noncommutative spectral geometry proposed by Connes as an approach to unification, is presented. It is ...
A new dynamical reflection algebra and related quantum integrable systems
new dynamical reflection algebra quantum integrable systems
2011/7/7
We propose a new dynamical reflection algebra, distinct from the previous dynamical boundary algebra and semi-dynamical reflection algebra. The associated Yang-Baxter equations, coactions, fusions, an...
A new dynamical reflection algebra and related quantum integrable systems
dynamical reflection algebra quantum integrable systems High Energy Physics Theory
2011/7/26
Abstract: We propose a new dynamical reflection algebra, distinct from the previous dynamical boundary algebra and semi-dynamical reflection algebra. The associated Yang-Baxter equations, coactions, f...
An Investigation on the Basic Conceptual Foundations of Quantum Mechanics by Using the Clifford Algebra
Clifford algebra, foundations of quantum mechanics, wave function collapse,quantum mechanics and conceptual entities, von Neumann postulates on quantum measurement
2011/9/2
We review our approach to quantum mechanics adding also some new interesting results. We start by giving proof of two important theorems ms on the existence of the A(Si) and i,±1 N Clifford algebras. ...
Homology of Lie algebra of supersymmetries and of super Poincare Lie algebra
Lie algebra supersymmetries super Poincare Lie algebra High Energy Physics - Theory
2011/7/27
Abstract: We study the homology and cohomology groups of super Lie algebra of supersymmetries and of super Poincare Lie algebra. We give complete answers for (non-extended) supersymmetry in all dimens...
Homological algebra modulo exact zero-divisors
Exact zero divisors (co)homology complexity
2011/1/21
We study the homological behavior of modules over local rings modulo exact zero-divisors. We obtain new results which are in some sense “opposite” to those known for modules over local rings modulo re...
Noncommutative oscillators from a Hopf algebra twist deformation. A first principles derivation
Noncommutative oscillators Hopf algebra twist deformation principles derivation
2011/3/3
Noncommutative oscillators are first-quantized through an abelian Drinfel’d twist deformation of a Hopf algebra and its action on a module. Several impor-tant and subtle issues making possible the qua...
Intertwining operators for Sklyanin algebra and elliptic hypergeometric series
Intertwining operators Sklyanin algebra elliptic hypergeometric series
2011/1/18
Intertwining operators for infinite-dimensional representations of the Sklyanin algebra with spins ℓ and −ℓ − 1 are constructed using the technique of intertwin-ing vectors for...
In this brief note we consider some bases in the Hecke algebra and exhibit certain dualities between them. Our results and arguments are completely combinatorial.However, to explain the motivation and...
This paper provides an explicit isomorphism between the Birman-Wenzl algebra BWn, constructed by J. Birman and H. Wenzl, and the Kauffman algebra MTn, subsequently constructed by H.R. Morton and P. Tr...
Algebra in superextensions of semilattices
semilattice band commutative semigroup the space of upfamilies
2011/1/20
Given a semilattice X we study the algebraic properties of the semigroup (X) of upfamilies on
X. The semigroup (X) contains the Stone-ˇCech extension (X), the superextension (X), and the space of...
Quadratic Algebra Approach to Relativistic Quantum Smorodinsky-Winternitz Systems
Quadratic Algebra Relativistic Quantum Smorodinsky-Winternitz Systems
2011/1/19
There exist a relation between the Klein-Gordon and the Dirac equations with scalar and vector potentials of equal magnitude (SVPEM) and the Schrödinger equation.
Elliptic dynamical reflection algebra and partition function of SOS model with reflecting end
Dynamical reflection algebra Boundary SOS model
2011/1/17
We introduce in this paper an elliptic dynamical reflection algebra describing an SOS model with reflecting end. Using factorizing Drinfel’d twist, we compute the partition function of this model with...