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Subalgebras of real three‐ and four‐dimensional Lie algebras

- J. Patera, P. Winternitz
- Mathematics
- 1 July 1977

The Lie subalgebras of all real Lie algebras of dimension d?4 are classified into equivalence classes under their groups of inner automorphisms. Tables of representatives of each conjugacy class are… Expand

Invariants of real low dimension Lie algebras

- J. Patera, R. Sharp, P. Winternitz, H. Zassenhaus
- Mathematics
- 1 June 1976

All invariant functions of the group generators (generalized Casimir operators) are found for all real algebras of dimension up to five and for all real nilpotent algebras of dimension six.

Continuous subgroups of the fundamental groups of physics. II. The similitude group

- J. Patera, P. Winternitz, H. Zassenhaus
- Mathematics
- 1 August 1975

All subalgebras of the similitude algebra (the algebra of the Poincare group extended by dilatations) are classified into conjugacy classes under transformations of the similitude group. Use is made… Expand

Orbit Functions

In the paper, properties of orbit functions are reviewed and further developed. Orbit functions on the Euclidean space En are symmetrized exponential functions. The symmetrization is fulfilled by a… Expand

Quasicrystals and icosians

A family of quasicrystals of dimensions 1, 2, 3, 4 governed by the root lattice E8 is constructed. The use of the icosian ring, found in the quaternions with coefficients in Q( square root 5), allows… Expand

Discrete and continuous graded contractions of Lie algebras and superalgebras

- M. Montigny, J. Patera
- Mathematics
- 7 February 1991

Grading preserving contractions of Lie algebras and superalgebras of any type over the complex number field are defined and studied. Such contractions fall naturally into two classes: the… Expand

Discrete and continuous graded contractions of representations of Lie algebras

Simultaneous grading of Lie algebras and their representation spaces is used to develop a new theory of grading preserving contractions of representations of all Lie algebras admitting the chosen… Expand

Antisymmetric Orbit Functions

In the paper, properties of antisymmetric orbit functions are reviewed and further developed. Antisymmetric orbit functions on the Euclidean space $E_n$ are antisymmetrized exponential functions.… Expand

E-Orbit Functions

We review and further develop the theory of E-orbit functions. They are func- tions on the Euclidean spaceEn obtained from the multivariate exponential function by sym- metrization by means of an… Expand

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