Related papers: Kauffman state sums and bracket deformation
One of the questions investigated in deformation theory is to determine to which algebras can a given associative algebra be deformed. In this paper we investigate a different but related question, namely: for a given associative…
We study a Lie algebra type $\kappa$-deformed space with undeformed rotation algebra and commutative vector-like Dirac derivatives in a covariant way. Space deformation depends on an arbitrary vector. Infinitely many covariant realizations…
For any given finite abelian group, we give factorizations of the group determinant in the group algebra of any subgroup. The factorizations are an extension of Dedekind's theorem. The extension leads to a generalization of Dedekind's…
Universal Deformation Formulas (UDFs) for the deformation of associative algebras play a key role in deformation quantization. Here we present examples for certain classes of infinitesimals. A basic representable 2-cocycle $F$ of an…
Suppose $R$ is a commutative ring with identity and a fixed invertible element $q^{\frac{1}{2}}$ such that $q+q^{-1}$ is invertible. For an oriented surface $\Sigma$, let $\mathcal{S}(\Sigma;R)$ denote the Kauffman bracket skein algebra of…
A star-product formalism describing deformations of the standard quantum mechanical harmonic oscillator is introduced. A number of existing generalized oscillators occur as particular choises of star-products between the elements of the…
We consider antiPoisson superalgebras realized on the smooth Grassmann-valued functions with compact supports in R^n and with the grading inverse to Grassmanian parity. The deformations of these superalgebras and their central extensions…
The double point relation defines a natural theory of algebraic cobordism for bundles on varieties. We construct a simple basis (over the rationals) of the corresponding cobordism groups over Spec(C) for all dimensions of varieties and…
Additive deformations of bialgebras in the sense of J. Wirth, i.e. deformations of the multiplication map fulfilling a certain compatibility condition w.r.t. the coalgebra structure, can be generalized to braided bialgebras. The theorems…
We study the biparametric quantum deformation of GL(2) x GL(1) and exhibit its cross-product structure. We derive explictly the associated dual algebra, i.e., the quantised universal enveloping algebra employing the R-matrix procedure. This…
We initiate the representation theory of the degenerate affine periplectic Brauer algebra on $n$ strands by constructing its finite-dimensional calibrated representations when $n=2$. We show that any such representation that is…
A class of vector states on a von Neumann algebra is constructed. These states belong to a deformed exponential family. One specific deformation is considered. It makes the exponential function asymptotically linear. Difficulties arising…
Given formal differential operators $F_i$ on polynomial algebra in several variables $x_1,...,x_n$, we discuss finding expressions $K_l$ determined by the equation $\exp(\sum_i x_i F_i)(\exp(\sum_j q_j x_j)) = \exp(\sum_l K_l x_l)$ and…
We construct a quadratic basis of generators of matrix-extended $\mathcal{W}_{1+\infty}$ using a generalization of the Miura transformation. This makes it possible to conjecture a closed-form formula for the operator product expansions…
We develop deformation theory of algebras over quadratic operads where the parameter space is a commutative local algebra. We also give a construction of a distinguised deformation of an algebra over a quadratic operad with a complete local…
The deformation quantization by Kontsevich [arXiv:q-alg/9709040] is a way to construct an associative noncommutative star-product $\star=\times+\hbar \{\ ,\ \}_{P}+\bar{o}(\hbar)$ in the algebra of formal power series in $\hbar$ on a given…
We propose a new formula for the star product in deformation quantization of Poisson structures related in a specific way to a variational problem for a function $S$, interpreted as the action functional. Our approach is motivated by…
The group algebras $kQ_{2^n}$ of the generalized quaternion groups $Q_{2^n}$ over fields $k$ which contain $\mathbb{F}_{2^{n-2}}$, are deformed to separable $k((t))$-algebras $[kQ_{2^n}]_t$. The dimensions of the simple components of…
For the fundamental representations of the simple Lie algebras of type $B_{n}$, $C_{n}$ and $D_{n}$, we derive the braiding and fusion matrices from the generalized Yang-Yang function and prove that the corresponding knot invariants are…
Deforming the algebraic structure of geometric algebra on the phase space with a Moyal product leads naturally to supersymmetric quantum mechanics in the star product formalism.