Contractions of Lie algebras and separation of variables. Two-dimensional hyperboloid

被引：19

作者：

Izmestev, AA ^{[1
]}

Pogosyan, GS ^{[1
]}

Sissakian, AN ^{[1
]}

Winternitz, P ^{[1
]}

机构：

[1] UNIV MONTREAL,CTR RECH MATH,MONTREAL,PQ H3C 3J7,CANADA

来源：

INTERNATIONAL JOURNAL OF MODERN PHYSICS A | 1997年 / 12卷 / 01期

关键词：

D O I：

10.1142/S0217751X97000074

中图分类号：

O57 [原子核物理学、高能物理学];

学科分类号：

070202 ;

摘要：

The Inonu-Wigner contraction from the Lorentz group O(2,1) to the Euclidean group E(2) is used to relate the separation of variables in the Laplace-Beltrami operators on the two corresponding homogeneous spaces. We consider the contractions on four levels: the Lie algebra, the commuting sets of second order operators in the enveloping algebra of o(2,1), the coordinate systems and some eigenfunctions of the Laplace-Beltrami operators.

引用

页码：53 / 61

页数：9

共 50 条

[41] Wildness of the problems of classifying two-dimensional spaces of commuting linear operators and certain Lie algebras
Futorny, Vyacheslav
Klymchuk, Tetiana
Petravchuk, Anatolii P.
Sergeichuk, Vladimir V.
LINEAR ALGEBRA AND ITS APPLICATIONS, 2018, 536 : 201 - 209
[42] Zero sets of Lie algebras of analytic vector fields on real and complex two-dimensional manifolds
Hirsch, Morris W.
Turiel, F-J
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2019, 39 : 954 - 979
[43] A new exactly solvable two-dimensional quantum model not amenable to separation of variables
Ioffe, M. V.
Nishnianidze, D. N.
Valinevich, P. A.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2010, 43 (48)
[44] The Classification of Two-dimensional Nonassociative Algebras
Petersson H.P.
Results in Mathematics, 2000, 37 (1-2) : 120 - 154
[45] Complete Classification of Two-Dimensional Algebras
Ahmed, Houida
Bekbaev, U.
Rakhimov, I.
4TH INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES (ICMS4): MATHEMATICAL SCIENCES: CHAMPIONING THE WAY IN A PROBLEM BASED AND DATA DRIVEN SOCIETY, 2017, 1830
[46] Dynamics of Two-Dimensional Evolution Algebras
Rozikov, U. A.
Murodov, Sh. N.
LOBACHEVSKII JOURNAL OF MATHEMATICS, 2013, 34 (04) : 344 - 358
[47] Two-dimensional Q-algebras
Nakazi, T
LINEAR ALGEBRA AND ITS APPLICATIONS, 2000, 315 (1-3) : 197 - 205
[48] Classification of two-dimensional Jordan algebras
Ahmed, Houida
Bekbaev, Ural
Rakhimov, Isamiddin
13TH IMT-GT INTERNATIONAL CONFERENCE ON MATHEMATICS, STATISTICS AND THEIR APPLICATIONS (ICMSA2017), 2017, 1905
[49] Two-dimensional categorified Hall algebras
Porta, Mauro
Sala, Francesco
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2023, 25 (03) : 1113 - 1205
[50] TWO-DIMENSIONAL SEPARATION PROCESSES
WANKAT, PC
SEPARATION SCIENCE AND TECHNOLOGY, 1984, 19 (11-1) : 801 - 829

← 1 2 3 4 5 →