Related papers: Colored Kac-Moody Algebras, Part I
The purpose of this paper is to study global deformations of Hom-Leibniz algebras. We introduce a cohomology for Hom-Leibniz algebras with values in a Hom-module, characterize versal deformations and provide examples.
We study the relationship between the transchromatic localizations of Morava $E$-theory, $L_{K(n-1)}E_n$, and formal groups. In particular, we show that the coefficient ring $\pi_0L_{K(n-1)}E_n$ has a modular interpretation, representing…
Thinking back the long history of physics, we see that the calculation used by physicists was nothing but the ordinary calculus. Another word, physicists have never wrote theories beyond the basic axioms of the calculus. This is not to…
Deformation quantization (the Moyal deformation) of SDYM equation for the algebra of the area preserving diffeomorphisms of a 2-surface $\Sigma_{2}$, sdiff($\Sigma_{2}$), is studied. Deformed equation we call the master equation (ME) as it…
We define a natural quantum analogue for the ${\cal Z}$ algebra, and which we refer to as the ${\cal Z}_q$ algebra, by modding out the Heisenberg algebra from the quantum affine algebra $U_q(\hat{sl(2)})$ with level $k$. We discuss the…
A vertex coloring of a simplicial complex $\Delta$ is called a linear coloring if it satisfies the property that for every pair of facets $(F_1, F_2)$ of $\Delta$, there exists no pair of vertices $(v_1, v_2)$ with the same color such that…
The main purpose of this paper is to define representations and a cohomology of color Hom-Lie algebras and to study some key constructions and properties. We describe Hartwig-Larsson-Silvestrov Theorem in the case of $\Gamma$-graded…
We consider the action of the Lie algebra of polynomial vector fields, $\mathfrak{vect}(1)$, by the Lie derivative on the space of symbols $\mathcal{S}_\delta^n=\bigoplus_{j=0}^n \mathcal{F}_{\delta-j}$. We study deformations of this…
The space of symbols of differential operators on a smooth manifold (i.e., the space of symmetric contravariant tensor fields) is naturally a module over the Lie algebra of vector fields. We study, in the case of $\bf R^n$ with $n\geq2$,…
Using homological perturbation theory, we develop a formal version of the miniversal deformation associated with a deformation problem controlled by a differential graded Lie algebra over a field of characteristic zero. Our approach…
Having in mind the significance of parity (reflection) in various areas of physics, the single-mode and two-mode Wigner algebras are considered adding to them a reflection operator. The associated deformed $sl(2, R)$ algebra,…
We construct explicit examples of half-sided modular inclusions ${\mathcal N}\subset{\mathcal M}$ of von Neumann algebras with trivial relative commutants. After stating a general criterion for triviality of the relative commutant in terms…
Algebraic deformations provide a systematic approach to generalizing the symmetries of a physical theory through the introduction of new fundamental constants. The applications of deformations of Lie algebras and Hopf algebras to both…
Let $\mathfrak{g}$ be a semi-simple Lie algebra with fixed root system, and $U_q(\mathfrak{g})$ the quantization of its universal enveloping algebra. Let $\mathcal{S}$ be a subset of the simple roots of $\mathfrak{g}$. We show that the…
The deformations of an infinite dimensional algebra may be controlled not just by its own cohomology but by that of an associated diagram of algebras, since an infinite dimensional algebra may be absolutely rigid in the classical…
We formulate several basic properties of Verma supermodules over regular symmetrizable Kac--Moody Lie superalgebras, exhibiting $\mathfrak{gl}(1|1)$-nature as revealed through changing Borel subalgebras. We investigate variants of Verma…
Based on our previous work on an arithmetic analogue of Christol's theorem, this paper studies in more detail the structure of the lambda-ring $E_K = K \otimes W_{O_K}^a (O_{\bar{K}})$ of algebraic Witt vectors for number fields $K$. First…
Let $\alpha$ be a quadratic Poisson bivector on a vector space $V$. Then one can also consider $\alpha$ as a quadratic Poisson bivector on the vector space $V^*[1]$. Fixed a universal deformation quantization (prediction some weights to all…
The main purpose of this article is to develop an explicit derived deformation theory of algebraic structures at a high level of generality, encompassing in a common framework various kinds of algebras (associative, commutative, Poisson...)…
A new infinite family of examples of finite non-bicolorable configurations of rays in Hilbert space is described. Such configurations appear in the analysis of quantum mechanics in terms of Bell's inequalities and Kochen-Specker theorem and…