Related papers: Two-photon algebra deformations
We discuss two-parameter deformations of an universal enveloping algebra $U(g[u])$ of a polynomial loop algebra $g[u]$, where $g$ is a finite-dimensional complex simple Lie algebra (or superalgebra). These deformations are Hopf algebras.…
We compute low-degree cohomology of current Lie algebras extended over the 3-dimensional simple algebra, compute deformations of related semisimple Lie algebras, and apply these results to classification of simple Lie algebras of absolute…
An elliptic two-parameter deformation of the (universal enveloping superalgebra of) affine Lie superalgebra $osp(1|2)^{(1)}$ is proposed in terms of free boson realization. This deformed superalgebra is shown to fit in the framework of…
Quantum algebras (also called quantum groups) are deformed versions of the usual Lie algebras, to which they reduce when the deformation parameter q is set equal to unity. From the mathematical point of view they are Hopf algebras. Their…
A theory of canonical basis for a two-parameter quantum algebra is developed in parallel with the one in one-parameter case. A geometric construction of the negative part of a two-parameter quantum algebra is given by using mixed perverse…
Any deformation of a Weyl or Clifford algebra can be realized through some change of generators in the undeformed algebra. Here we briefly describe and motivate our systematic procedure for constructing all such changes of generators for…
We discuss quantum deformation of the affine transformation algebra. It is shown that the quantum algebra has a non-cocommutative Hopf algebra structure, simple realizations and quantum tensor operators.
For a given finite dimensional Hopf algebra $H$ we describe the set of all equivalence classes of cocycle deformations of $H$ as an affine variety, using methods of geometric invariant theory. We show how our results specialize to the…
We study non-trivial deformations of the natural imbedding of the Lie algebra $\fh_1$ of lower triangular matrices (the Heisenberg Lie algebra) into $gl(3,\mathbb{K})$, where $\mathbb{K}=\mathbb{R}$ or $|mathbb{C}$. Our first result is the…
The algebra of diffeomorphisms derived from general coordinate transformations on commuting coordinates is represented by differential operators on noncommutative spaces. The algebra remains unchanged, the comultiplication however is…
We describe three ways of modifying the relativistic Heisenberg algebra - first one not linked with quantum symmetries, second and third related with the formalism of quantum groups. The third way is based on the identification of…
All deformations of two dimensional centrally extended Galilei group are classified. The corresponding quantum Lie algebras are found.
We study the scalar quantum field theory on a generic noncommutative two-sphere as a special case of noncommutative curved space, which is described by the deformation quantization algebra obtained from symplectic reduction and parametrized…
The $L_\infty$-algebra is an algebraic structure suitable for describing deformation problems. In this paper we construct one $L_\infty$-algebra, which turns out to be a differential graded Lie algebra, to control the deformations of Lie…
Let $k$ be a field of characteristic zero, $\CO$ be a dg operad over $k$ and let $A$ be an $\CO$-algebra. In this note we define formal deformations of $A$, construct the deformation functor $$\Def_A:\dgar(k)\to\simpl$$ from the category of…
We construct the deformation functor associated to a couple of morphisms of differential graded Lie algebras, and use it to study the infinitesimal deformations of a holomorphic map of compact complex manifolds. In particular, in the case…
A systematic computational approach for the explicit construction of any quantum Hopf algebra (U_z(g),\Delta_z) starting from the Lie bialgebra (g,\delta) that gives the first-order deformation of the coproduct map \Delta_z is presented.…
Algebraic quantum field theory is considered from the perspective of the Hochschild cohomology bicomplex. This is a framework for studying deformations and symmetries. Deformation is a possible approach to the fundamental challenge of…
Clifford geometric algebras of multivectors are introduced which exhibit a bilinear form which is not necessarily symmetric. Looking at a subset of bi-vectors in CL(K^{2n},B), we proof that theses elements generate the Hecke algebra…
Deformed orthogonal and pseudo-orthogonal Lie algebras are constructed which differ from deformations of Lie algebras in terms of Cartan subalgebra and root vectors and which make it possible to construct representations by operators acting…