On the algebra of symmetries of Laplace and Dirac operators
 Author
 Hendrik De Bie (UGent) , Roy Oste (UGent) and Joris Van der Jeugt (UGent)
 Organization
 Abstract
 We consider a generalization of the classical Laplace operator, which includes the LaplaceDunkl operator defined in terms of the differentialdifference operators associated with finite reflection groups called Dunkl operators. For this Laplacelike operator, we determine a set of symmetries commuting with it, in the form of generalized angular momentum operators, and we present the algebraic relations for the symmetry algebra. In this context, the generalized Dirac operator is then defined as a square root of our Laplacelike operator. We explicitly determine a family of graded operators which commute or anticommute with our Diraclike operator depending on their degree. The algebra generated by these symmetry operators is shown to be a generalization of the standard angular momentum algebra and the recently defined higherrank BannaiIto algebra.
 Keywords
 BANNAIITO ALGEBRA, DUNKL OPERATORS, EQUATIONS, Laplace operator, Dirac operator, Dunkl operator, Symmetry algebra, BannaiIto algebra
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Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU8567845
 Chicago
 De Bie, Hendrik, Roy Oste, and Joris Van der Jeugt. 2018. “On the Algebra of Symmetries of Laplace and Dirac Operators.” Letters in Mathematical Physics 108 (8): 1905–1953.
 APA
 De Bie, H., Oste, R., & Van der Jeugt, J. (2018). On the algebra of symmetries of Laplace and Dirac operators. LETTERS IN MATHEMATICAL PHYSICS, 108(8), 1905–1953.
 Vancouver
 1.De Bie H, Oste R, Van der Jeugt J. On the algebra of symmetries of Laplace and Dirac operators. LETTERS IN MATHEMATICAL PHYSICS. 2018;108(8):1905–53.
 MLA
 De Bie, Hendrik, Roy Oste, and Joris Van der Jeugt. “On the Algebra of Symmetries of Laplace and Dirac Operators.” LETTERS IN MATHEMATICAL PHYSICS 108.8 (2018): 1905–1953. Print.
@article{8567845, abstract = {We consider a generalization of the classical Laplace operator, which includes the LaplaceDunkl operator defined in terms of the differentialdifference operators associated with finite reflection groups called Dunkl operators. For this Laplacelike operator, we determine a set of symmetries commuting with it, in the form of generalized angular momentum operators, and we present the algebraic relations for the symmetry algebra. In this context, the generalized Dirac operator is then defined as a square root of our Laplacelike operator. We explicitly determine a family of graded operators which commute or anticommute with our Diraclike operator depending on their degree. The algebra generated by these symmetry operators is shown to be a generalization of the standard angular momentum algebra and the recently defined higherrank BannaiIto algebra.}, author = {De Bie, Hendrik and Oste, Roy and Van der Jeugt, Joris}, issn = {03779017}, journal = {LETTERS IN MATHEMATICAL PHYSICS}, language = {eng}, number = {8}, pages = {19051953}, title = {On the algebra of symmetries of Laplace and Dirac operators}, url = {http://dx.doi.org/10.1007/s1100501810650}, volume = {108}, year = {2018}, }
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