scholarly journals The Hopf algebra structure of the Z3-graded quantum supergroup GLq,j(1∣1)

2008 ◽  
Vol 49 (2) ◽  
pp. 023511 ◽  
Author(s):  
Salih Celik ◽  
Ergün Yasar
Keyword(s):  
Hopf Algebra ◽  
Algebra Structure ◽  
Hopf Algebra Structure ◽  
Quantum Supergroup

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.

The Hopf algebra structure of the h-deformed Z3-graded quantum supergroup GLh,j(1|1)

2016 ◽  
Vol 13 (07) ◽  
pp. 1650103
Author(s):  
Ergün Yasar
Keyword(s):  
Hopf Algebra ◽  
Algebra Structure ◽  
Hopf Algebra Structure ◽  
Quantum Supergroup ◽  
New Formula

In this work, we define a new proper singular [Formula: see text] matrix to construct a Z3-graded calculus on the [Formula: see text]-deformed quantum superplane. Using the obtained calculus, we construct a new [Formula: see text]-deformed Z3-graded quantum supergroup and give some features of it. Finally, we build up the Hopf algebra structure of this supergroup.

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.

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