Twists of quantum groups and noncommutative field theory

Kulish, P. P.

doi:10.1007/s10958-007-0166-6

Cited by 17 publications

(35 citation statements)

References 27 publications

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“…For quantum twist deformations of enveloping Lie algebras U(g) (g = o(4; C), o(4 − k, k) (k = 0, 1, 2), and o * (4) = 0(2; H)); for o(4; C) (see section 5.1, 5.2) the algebra of quantum modules, describing e.g. NC quantum fields, can be represented by the functions of commutative classical fields with twist-dependent nonlocal star product multiplication rule [66,67]. The D = 4 Minkowski space R 3,1 , with signature (+, +, +, −), and its Lorentz rotations o(3, 1) play basic role in relativistic physics.…”

Section: Jhep11(2017)187mentioning

confidence: 99%

Basic quantizations of D = 4 Euclidean, Lorentz, Kleinian and quaternionic $$ {\mathfrak{o}}^{\star }(4) $$ symmetries

Borowiec¹,

Lukierski²,

Tolstoy³

2017

J. High Energ. Phys.

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We construct firstly the complete list of five quantum deformations of D = 4 complex homogeneous orthogonal Lie algebra o(4; C) ∼ = o(3; C) ⊕ o(3; C), describing quantum rotational symmetries of four-dimensional complex space-time, in particular we provide the corresponding universal quantum R-matrices. Further applying four possible reality conditions we obtain all sixteen Hopf-algebraic quantum deformations for the real forms of o(4; C): Euclidean o(4), Lorentz o(3, 1), Kleinian o(2, 2) and quaternionic o ⋆ (4). For o(3, 1) we only recall well-known results obtained previously by the authors, but for other real Lie algebras (Euclidean, Kleinian, quaternionic) as well as for the complex Lie algebra o(4; C) we present new results.

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Section: Jhep11(2017)187mentioning

confidence: 99%

Basic quantizations of D = 4 Euclidean, Lorentz, Kleinian and quaternionic $$ {\mathfrak{o}}^{\star }(4) $$ symmetries

Borowiec¹,

Lukierski²,

Tolstoy³

2017

J. High Energ. Phys.

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“…We further assume that the Hermitean conjugation Q a α → (Q a α ) ⋆ ,Q ȧ α → (Q ȧ α ) ⋆ is well defined. 10 Then one can formulate N=2 Euclidean superalgebra in a Hermitean form if we impose the subsidiary condition which follows from (3.24) (α = 1,2; a,b = 1,2) 7) or more explicitly…”

Section: N=2 (Pseudo) Real Super-euclidean R-matricesmentioning

confidence: 99%

Real and pseudoreal forms of D=4 complex Euclidean (super)algebras and super-Poincaré/ super-Euclidean r-matrices

Borowiec

Lukierski

Tolstoy

2016

J. Phys.: Conf. Ser.

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We provide the classification of real forms of complex D=4 Euclidean algebra ε(4; C) = o(4; C))⋉T 4 C as well as (pseudo)real forms of complex D=4 Euclidean superalgebras ε(4 N; C) for N=1,2. Further we present our results: N=1 and N=2 supersymmetric D=4 Poincaré and Euclidean r-matrices obtained by using D= 4 Poincaré r-matrices provided by Zakrzewski [1] For N=2 we shall consider the general superalgebras with two central charges. 2 We point out here that among 21 classical r−matrices obtained by Zakrzewski [1] there is one class which satisfies modified YB equation. We shall consider 20 classes of r−matrices which lead to triangular deformations.

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“…If the algebra (4.1) is associated with twisted A i -symmetries defined by a twist F the multiplication of noncommutative coordinatesx µ can be isomorphically represented by suitable star multiplication of the commuting classical coordinates 5) JHEP06 (2012)154 where W denotes the Weyl map, defined for the twist factor F by the formula (see [9]- [13])…”

Section: Twist Deformations Of (Super)space-timementioning

confidence: 99%

$ N = \frac{1}{2} $ deformations of chiral superspaces from new quantum Poincaré and Euclidean superalgebras

Borowiec

Lukierski

Mozrzymas

et al. 2012

J. High Energ. Phys.

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We present a large class of supersymmetric classical r-matrices, describing the supertwist deformations of Poincaré and Euclidean superalgebras. We consider in detail new family of four supertwists of N = 1 Poincaré superalgebra and provide as well their Euclidean counterpart. The proposed supertwists are better adjusted to the description of deformed D = 4 Euclidean supersymmetries with independent left-chiral and right-chiral supercharges. They lead to new quantum superspaces, obtained by the superextension of twist deformations of spacetime providing Lie-algebraic noncommutativity of space-time coordinates. In the Hopf-algebraic Euclidean SUSY framework the considered supertwist deformations provide an alternative to the N = 1 2 SUSY Seiberg's star product deformation scheme.

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Twists of quantum groups and noncommutative field theory

Cited by 17 publications

References 27 publications

Basic quantizations of D = 4 Euclidean, Lorentz, Kleinian and quaternionic $$ {\mathfrak{o}}^{\star }(4) $$ symmetries

Basic quantizations of D = 4 Euclidean, Lorentz, Kleinian and quaternionic $$ {\mathfrak{o}}^{\star }(4) $$ symmetries

Real and pseudoreal forms of D=4 complex Euclidean (super)algebras and super-Poincaré/ super-Euclidean r-matrices

$ N = \frac{1}{2} $ deformations of chiral superspaces from new quantum Poincaré and Euclidean superalgebras

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