Quasi-Deformations of sl_2(\F) using twisted derivations

By Daniel S. D. Larsson, Sergei Silvestrov. 2005

102 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/152e78de2152cec5223011968532c8128f079026

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Abdenacer Makhlouf
2. Donald Yau
3. Aron Gohr
4. Yael Fregier
5. Florin Panaite
6. F. Ammar
7. Y. Sheng
8. S. Benayadi

Citations in the corpus

• HOM-ALTERNATIVE ALGEBRAS AND HOM-JORDAN ALGEBRAS (2009, methodology): “The Hom-Lie algebras were introduced and discussed in [12, 15, 16, 17], motivated by quasi-deformations of Lie algebras of vector fields, in particular q-deformations of Witt and Virasoro algebras.”
• Unital algebras of Hom-associative type and surjective or injective twistings (2009, background): “In [7, 8, 12], quasi-Hom-Lie algebras, the general quasi-Lie algebras, and the corresponding generalization of Leibniz algebras quasi-Leibniz algebras [9] have been introduced.”
• On Hom-algebra structures (2006, background): “tity then one gets the classical Lie algebras sl(2). Remark 5.2. It would be interesting to compare this list with the quasi-hom-Lie and Hom-Lie algebras of quasi-deformations of sl(2) constructed in [6] using a quasi-hom-Lie structure on twisted vector fields. We provide in the following a list of a”
• Hom-Lie Algebras with Symmetric Invariant NonDegenerate Bilinear Forms (2010, unknown): “A general study and construction of Hom-Lie algebras are considered in [20, 25, 26] and a more general framework bordering color and super Lie algebras was introduced in [20, 25, 26, 27].”
• Yetter-Drinfeld modules for Hom-bialgebras (2013, methodology): “Motivated by these examples and their generalization, Hartwig, Larsson and Silvestrov in [17, 21, 22, 23] introduced the notion of Hom-Lie algebra as a deformation of Lie algebras in which the Jacobi identity is twisted by a homomorphism.”
• Hom-bialgebras and comodule Hom-algebras (2008, background): “Hom-Lie algebras are also related to deformed vector fields [8,13,14,15,22,23], number theory [12], the various versions of the Yang-Baxter equations, braid group representations, and quantum groups [28] - [35].”
• Paradigm of Nonassociative Hom-algebras and Hom-superalgebras (2010, methodology): “This family of HomLie algebras was constructed in [29] using a quasi-deformation scheme based on discretizing by means of Jackson q-derivations a representation of sl2(K) by onedimensional vector fields (first order ordinary differential operators) and using the twisted commutator bracket defined in”