Related papers: New Universal Deformation Formulas for deformation…
We consider finite-dimensional complex Lie algebras. Using certain complex parameters we generalize the concept of cohomology cocycles of Lie algebras. A special case is generalization of 1-cocycles with respect to the adjoint…
In these lecture notes I give an introduction to deformation quantization. The quantization problem is discussed in some detail thereby motivating the notion of star products. Starting from a deformed observable algebra, i.e. the star…
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…
Any deformation of a Weyl or Clifford algebra A can be realized through a `deforming map', i.e. a formal change of generators in A. This is true in particular if A is covariant under a Lie algebra g and its deformation is induced by some…
It is outlined how deformations of field theoretical rigid symmetries can be constructed and classified by cohomological means in the extended antifield formalism. Special attention is devoted to deformations referring only to a subset of…
The diffeomorphism symmetry of general relativity leads in the canonical formulation to constraints, which encode the dynamics of the theory. These constraints satisfy a complicated algebra, known as Dirac's hypersurface deformation…
We show that deformed Heisenberg algebra with reflection emerging in parabosonic constructions is also related to parafermions. This universality is discussed in different algebraic aspects and is employed for the description of spin-j…
A two-parametric deformation of U[sl(2)] and its representations are considered. This newly introduced two-parametric quantum group denoted as $U_{pq}[sl(2)]$ admits a class of infinite-dimensional representations which have no classical…
We develop the deformation-obstruction calculus for morphisms of complexes with a fixed lift of the codomain, to derived categories of flat nilpotent deformations of abelian categories. As an application, we give an alternative proof that…
In this paper we construct a deformation quantization of the algebra of polynomials of an arbitrary (regular and non regular) coadjoint orbit of a compact semisimple Lie group. The deformed algebra is given as a quotient of the enveloping…
Aspects of the algebraic structure and representation theory of the quantum affine superalgebras with symmetrizable Cartan matrices are studied. The irreducible integrable highest weight representations are classified, and shown to be…
Let $\Bbbk$ be an algebraically closed field and $\Lambda$ a generalized Brauer tree algebra over $\Bbbk$. We compute the universal deformation rings of the periodic string modules over $\Lambda$. Moreover, for a specific class of…
In this paper we present a novel representation for deformation fields of 3D shapes, by considering the induced changes in the underlying metric. In particular, our approach allows to represent a deformation field in a coordinate-free way…
The paper gives the sufficient condition formulated in the syntactical form for all codescent morphisms of a variety of universal algebras satisfying the amalgamation property to be effective. This result is further used in proving that all…
QFTs with local topological operators feature unusual sectors called "universes," which are separated by infinite-tension domain walls. We show that such systems have relevant deformations with exactly-calculable effects. These deformations…
By using cocycle deformation, we construct a certain class of Hopf algebras, containing the quantized enveloping algebras and their analogues, from what we call pre-Nichols algebras. Our construction generalizes in some sense the known…
For a certain class of Lie bialgebras $(A,A^*)$ the corresponding quantum universal enveloping algebras $U_q(A)$ are prooved to be equivalent to quantum groups Fun$_q(F^*)$, $F^*$ being the factor group for the dual group $G^*$. This…
A description of a ring of functions on the base of a universal formal deformation for several moduli problems is given. The answer is given in terms of a homology group of a certain dg Lie algebra canonically (up to an essentially unique…
In this paper we provide an explicit construction of star products on U(g)-module algebras by using the Fedosov approach. This construction allows us to give a constructive proof to Drinfel'd theorem and to obtain a concrete formula for…
Phase-space realisations of an infinite parameter family of quantum deformations of the boson algebra in which the $q$-- and the $qp$--deformed algebras arise as special cases are studied. Quantum and classical models for the corresponding…