A Rodriguez formula and integration measure for the quantum deformed Legendre functions
Quantum deformed analogs of the Legendre functions are constructed from shift operator representations of the quantum deformed orbital angular momentum operators. A Rodriguez formula is found as well ...
Quantum deformed analogs of the Legendre functions are constructed from shift operator representations of the quantum deformed orbital angular momentum operators. A Rodriguez formula is found as well ...
Comment on: The Itzykson–Zuber integral for U(m|n) [J. Math. Phys. 36, 3085–3093 (1995)]
Abstract space–times and their Lorentz groups
J. Math. Phys. 37, 3073 (1996); doi:10.1063/1.531555
Issue Date: June 1996
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It has recently been discovered [A. A. Ungar, Am. J. Phys. 59, 824 (1991); 60, 815 (1992)] that the set R
={v![[is-an-element-of]](http://scitation.aip.org/stockgif3/isin.gif)
R3 : 
v<c} of all relativistically admissible velocities in Euclidean three-space R3, with a binary operation ![[direct-sum]](http://scitation.aip.org/stockgif3/oplus.gif)
given by relativistic velocity addition, forms a gyrogroup (R,). The gyrogroup (R,) reduces to the group (R3,+) in the limit c
![[infinity]](http://scitation.aip.org/stockgif3/infin.gif)
, + being the prerelativistic velocity addition (that is, the ordinary vector addition in the Euclidean three-space R3). The binary operation in R is gyroassociative and gyrocommutative, as opposed to the binary operation + in R3 which is associative and commutative. In this article we extend the study of gyrogroups into that of Lorentz groups. In particular, we find that a gyrogroup must be equipped with a cocycle form in order to be extendible into a Lorentz group. We thus study gyrogroups that are equipped with a cocycle form, and their resulting Lorentz groups. Interestingly, the cocycle form needed for the extension of gyrogroups into Lorentz groups involves a cocycle identity which is known to be useful in various branches of mathematics [B. R. Ebanks and C. T. Ng, Aequat. Math. 46, 76 (1993)]. ©1996 American Institute of Physics.
R3 : v<c} of all relativistically admissible velocities in Euclidean three-space R3, with a binary operation given by relativistic velocity addition, forms a gyrogroup (R). The gyrogroup (R) reduces to the group (R3,+) in the limit c, + being the prerelativistic velocity addition (that is, the ordinary vector addition in the Euclidean three-space R3). The binary operation in R| History: | Received 26 September 1994; accepted 20 February 1996 |
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0022-2488 (print)
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REFERENCES (18)
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