A Two-parameter bicovariant differential calculus on the (1 + 2)-dimensional q-superspace

2016 ◽  
Vol 13 (03) ◽  
pp. 1650029
Author(s):  
Ergün Yasar
Keyword(s):  
Hopf Algebra ◽  
Differential Calculus ◽  
Lie Superalgebra ◽  
Point Of View ◽  
Algebra Structure ◽  
Hopf Algebra Structure ◽  
Bicovariant Differential Calculus ◽  
Two Parameter

We construct a two-parameter bicovariant differential calculus on [Formula: see text] with the help of the covariance point of view using the Hopf algebra structure of [Formula: see text]. To achieve this, we first use the consistency of calculus and the approach of [Formula: see text]-matrix which satisfies both ungraded and graded Yang–Baxter equations. In particular, based on this differential calculus, we investigate Cartan–Maurer forms for this [Formula: see text]-superspace. Finally, we obtain the quantum Lie superalgebra corresponding the Cartan–Maurer forms.

Bicovariant differential calculus on the quantum superspace ℝq(1|2)

2016 ◽  
Vol 15 (09) ◽  
pp. 1650172 ◽  
Author(s):  
Salih Celik
Keyword(s):  
Hopf Algebra ◽  
Differential Calculus ◽  
Vector Fields ◽  
Lie Superalgebra ◽  
Function Algebra ◽  
Algebra Structure ◽  
Hopf Algebra Structure ◽  
Bicovariant Differential Calculus ◽  
Quantum Supergroup ◽  
Dual Hopf Algebra

Super-Hopf algebra structure on the function algebra on the extended quantum superspace has been defined. It is given a bicovariant differential calculus on the superspace. The corresponding (quantum) Lie superalgebra of vector fields and its Hopf algebra structure are obtained. The dual Hopf algebra is explicitly constructed. A new quantum supergroup that is the symmetry group of the differential calculus is found.

HOPF ALGEBRA STRUCTURE OF (2+1)-DIMENSIONAL QUANTUM SUPERSPACE, ITS DUAL AND ITS DIFFERENTIAL CALCULUS

2010 ◽  
Vol 25 (26) ◽  
pp. 2241-2253 ◽  
Author(s):  
MUTTALIP OZAVSAR
Keyword(s):  
Hopf Algebra ◽  
Differential Calculus ◽  
Lie Superalgebra ◽  
Algebra Structure ◽  
Hopf Superalgebra ◽  
Hopf Algebra Structure ◽  
Quantum Supergroup ◽  
Noncommuting Coordinates

We consider a (2+1)-dimensional quantum superspace which has noncommuting coordinates in Manin sense and it was shown that this space has a Hopf algebra structure, i.e. the quantum supergroup, when it is extended by the inverse of the bosonic variable. Differential structures on this space were given by constructing the differential calculus in the sense of Woronowicz. Thus, we deduce that the corresponding quantum Lie superalgebra which as a commutation superalgebra appears classical, and as Hopf structure is non-cocommutative q-deformed. Finally, dual Hopf superalgebra was given.

Some Results in the Connective K-Theory of Lie Groups

1988 ◽  
Vol 31 (2) ◽  
pp. 194-199
Author(s):  
L. Magalhães
Keyword(s):  
Hopf Algebra ◽  
Lie Groups ◽  
Lie Group ◽  
Algebra Structure ◽  
Hopf Algebra Structure ◽  
K Theory ◽  
Torsion Free ◽  
Connected Lie Group

AbstractIn this paper we give a description of:(1) the Hopf algebra structure of k*(G; L) when G is a compact, connected Lie group and L is a ring of type Q(P) so that H*(G; L) is torsion free;(2) the algebra structure of k*(G2; L) for L = Z2 or Z.

scholarly journals ON THE COALGEBRAIC RING AND BOUSFIELD–KAN SPECTRAL SEQUENCE FOR A LANDWEBER EXACT SPECTRUM

2004 ◽  
Vol 47 (3) ◽  
pp. 513-532 ◽  
Author(s):  
Martin Bendersky ◽  
John R. Hunton
Keyword(s):  
Hopf Algebra ◽  
Spectral Sequence ◽  
Adams Spectral Sequence ◽  
Subject Classification ◽  
Homotopy Groups ◽  
Algebra Structure ◽  
Simple Description ◽  
Ring Spectrum ◽  
Hopf Algebra Structure

AbstractWe construct a Bousfield–Kan (unstable Adams) spectral sequence based on an arbitrary (and not necessarily connective) ring spectrum $E$ with unit and which is related to the homotopy groups of a certain unstable $E$ completion $X_E^{\wedge}$ of a space $X$. For $E$ an $\mathbb{S}$-algebra this completion agrees with that of the first author and Thompson. We also establish in detail the Hopf algebra structure of the unstable cooperations (the coalgebraic module) $E_*(\underline{E}_*)$ for an arbitrary Landweber exact spectrum $E$, extending work of the second author with Hopkins and with Turner and giving basis-free descriptions of the modules of primitives and indecomposables. Taken together, these results enable us to give a simple description of the $E_2$-page of the $E$-theory Bousfield–Kan spectral sequence when $E$ is any Landweber exact ring spectrum with unit. This extends work of the first author and others and gives a tractable unstable Adams spectral sequence based on a $v_n$-periodic theory for all $n$.AMS 2000 Mathematics subject classification: Primary 55P60; 55Q51; 55S25; 55T15. Secondary 55P47

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