Non-abelian tensor and exterior products modulo $q$ and universal $q$-central relative extension of Lie algebras
نویسندگان
چکیده
منابع مشابه
q-deformed Lie algebras and fractional calculus
Fractional calculus and q-deformed Lie algebras are closely related. Both concepts expand the scope of standard Lie algebras to describe generalized symmetries. For the fractional harmonic oscillator, the corresponding q-number is derived. It is shown, that the resulting energy spectrum is an appropriate tool e.g. to describe the ground state spectra of even-even nuclei. In addition, the equiva...
متن کاملTensor Algebras, Symmetric Algebras and Exterior Algebras
We begin by defining tensor products of vector spaces over a field and then we investigate some basic properties of these tensors, in particular the existence of bases and duality. After this, we investigate special kinds of tensors, namely, symmetric tensors and skew-symmetric tensors. Tensor products of modules over a commutative ring with identity will be discussed very briefly. They show up...
متن کاملTensor, Exterior and Symmetric Algebras
3 The Exterior Algebra 6 3.1 Dimension of the Exterior Powers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 Bilinear Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.3 Other Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.3.1 The determinant formula . . . . . . . . . . . . . . . . . . . . . . . . . ...
متن کاملQuantum Lie algebras , their existence , uniqueness and q -
Quantum Lie algebras are generalizations of Lie algebras which have the quantum parameter h built into their structure. They have been defined concretely as certain submodules Lh(g) of the quantized enveloping algebras Uh(g). On them the quantum Lie product is given by the quantum adjoint action. Here we define for any finite-dimensional simple complex Lie algebra g an abstract quantum Lie alge...
متن کاملQuantum Lie algebras , their existence , uniqueness and q - antisymmetry
Quantum Lie algebras are generalizations of Lie algebras which have the quantum parameter h built into their structure. They have been defined concretely as certain submodules Lh(g) of the quantized enveloping algebras Uh(g). On them the quantum Lie bracket is given by the quantum adjoint action. Here we define for any finite-dimensional simple complex Lie algebra g an abstract quantum Lie alge...
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ژورنال
عنوان ژورنال: Homology, Homotopy and Applications
سال: 1999
ISSN: 1532-0073,1532-0081
DOI: 10.4310/hha.1999.v1.n1.a9