Fractional superLie algebras and groups

Ahmedov, H.; Yıldız, Ali; Ucan, Yasemen

doi:10.1088/0305-4470/34/33/306

Cited by 12 publications

(30 citation statements)

References 11 publications

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“…In [28], the vectorial description of U(g) * does not correspond to the result of proposition 3. In fact, in this paper, the authors do not use Roby algebras to describe the dual of the enveloping algebra.…”

Section: Dual Of the Hopf Algebra Associated To Lie Algebras Of Ordermentioning

confidence: 93%

Hopf algebras for ternary algebras

Goze

Traubenberg

2009

Journal of Mathematical Physics

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We construct an universal enveloping algebra associated to the ternary extension of Lie (super)algebras called Lie algebra of order three. A Poincaré-Birkhoff-Witt theorem is proven is this context. It this then shown that this universal enveloping algebra can be endowed with a structure of Hopf algebra. The study of the dual of the universal enveloping algebra enables to define the parameters of the transformation of a Lie algebra of order three. It turns out that these variables are the variables which generate the three-exterior algebra.

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Section: Dual Of the Hopf Algebra Associated To Lie Algebras Of Ordermentioning

confidence: 93%

Hopf algebras for ternary algebras

Goze

Traubenberg

2009

Journal of Mathematical Physics

View full text Add to dashboard Cite

show abstract

“…Let U ( g ) be the universal enveloping algebra of a Lie algebra g generated by Y j , j = 1, 2, …, dim ( g ) with

([],, X_{i}, X_{j}) = \sum_{k = 1}^{italicdim ((), g)} c_{ij}^{k} X_{k},

where

c_{ij}^{k}

are the structure constants given Lie algebra g . The Hopf algebra of the universal enveloping algebra U ( g ) is given as follows in Ahmedov et al:

\begin{matrix} lefttrue \\ Δ : U (g) \to U (g) \otimes U (g), Δ (Y_{j}) = Y_{j} \otimes 1 + 1 \otimes Y_{j}, \\ ε : U (g) \to C, \dots ε (Y_{j}) = 0, \\ S : U (g) \to U (g), \dots S (Y_{j}) = - Y_{j} . \end{matrix}

…”

Section: Preliminary Information On Fractional Supersymmetric Algebrasmentioning

confidence: 99%

“…Fractional supersymmetric algebras are generalized forms of supersymmetric Lie algebras. There are many methods to obtain fractional supersymmetric algebras . Considering the importance and popularity of the algebra su (2), the idea arose of applying the form of fractional superalgebra to su (2).…”

Section: Introductionmentioning

confidence: 99%