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Algebras and Representation Theory, 2001
Let \(V\) be a vector space and let \(c: V \otimes V \to V \otimes V\) be a solution of the braid equation: \((c\otimes \text{id})(\text{id} \otimes c)(c\otimes \text{id}) = (\text{id} \otimes c)(c\otimes \text{id}) (\text{id} \otimes c)\). There is a remarkable braided graded Hopf algebra \(\mathfrak B (V) = \oplus_{n \geq 0} \mathfrak B^n(V)\), which
Flores de Chela, Delia, Green, James A.
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Let \(V\) be a vector space and let \(c: V \otimes V \to V \otimes V\) be a solution of the braid equation: \((c\otimes \text{id})(\text{id} \otimes c)(c\otimes \text{id}) = (\text{id} \otimes c)(c\otimes \text{id}) (\text{id} \otimes c)\). There is a remarkable braided graded Hopf algebra \(\mathfrak B (V) = \oplus_{n \geq 0} \mathfrak B^n(V)\), which
Flores de Chela, Delia, Green, James A.
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The p-adic quantum plane algebras and quantum Weyl algebra
P-Adic Numbers, Ultrametric Analysis, and Applications, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Diarra, Bertin, Tangara, Fana
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Studia Logica, 1996
The infinite-valued logic \(L_\infty\) (Lukasiewicz logic) was introduced as a generalization of classical logic. \textit{C. C. Chang} [Trans. Am. Math. Soc. 88, 467-490 (1958; Zbl 0084.00704)] introduced MV algebras in order to provide an algebraic proof of its completeness theorem.
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The infinite-valued logic \(L_\infty\) (Lukasiewicz logic) was introduced as a generalization of classical logic. \textit{C. C. Chang} [Trans. Am. Math. Soc. 88, 467-490 (1958; Zbl 0084.00704)] introduced MV algebras in order to provide an algebraic proof of its completeness theorem.
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Mathematical Proceedings of the Cambridge Philosophical Society, 1926
For the purposes of atomic physics it has been found convenient to introduce the idea of quantities that do not in general satisfy the commutative law of multiplication, but satisfy all the other laws of ordinary algebra. These quantities are called q-numbers, and the numbers of ordinary mathematics c-numbers, while the word number alone is used to ...
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For the purposes of atomic physics it has been found convenient to introduce the idea of quantities that do not in general satisfy the commutative law of multiplication, but satisfy all the other laws of ordinary algebra. These quantities are called q-numbers, and the numbers of ordinary mathematics c-numbers, while the word number alone is used to ...
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Quantum Algebras for Quantum Optics
2003Many models in Quantum Optics, such as two- and three-wave mixing and interaction of two-level atoms with a single-mode radiation field (Dicke model), can be described by interaction Hamiltonians of the form $$ H = \left( \begin{gathered} 0 {A_l} 0 \ldots 0 \hfill \\ {A_l} 0 {A_{{l - 1}}} \ldots 0 \hfill \\ \ldots \ldots \ldots \ldots \ldots \hfill
S. M. Chumakov, A. Ballesteros
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Il Nuovo Cimento B Series 11, 1994
The non-compact, metrically indefinite structures in the ghost formulation of gauge theories can be related to the tangent description of the underlying symmetry group. The algebraic origin of those nilpotent degrees of freedom and their quantized formulation are discussed generally in the connection of the complex representations of a compact group ...
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The non-compact, metrically indefinite structures in the ghost formulation of gauge theories can be related to the tangent description of the underlying symmetry group. The algebraic origin of those nilpotent degrees of freedom and their quantized formulation are discussed generally in the connection of the complex representations of a compact group ...
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Generalization of Drinfeld Quantum Affine Algebras
Letters in Mathematical Physics, 1997Kenji Iohara, Jintai Ding
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