TY - JOUR

T1 - Outer automorphisms of sl(2), integrable systems, and mappings

AU - Tsyganov, A. V.

PY - 1999/1/1

Y1 - 1999/1/1

N2 - Outer automorphisms of infinite-dimensional representations of the Lie algebra sl(2) are used to construct Lax matrices for integrable Hamiltonian systems and discrete integrable mappings. The known results are reproduced, and new integrable systems are constructed. Classical r-matrices corresponding to the Lax representation with the spectral parameter are dynamic. This scheme is advantageous because quantum systems naturally arise in the framework of the classical r-matrix Lax representation and the corresponding quantum mechanical problem admits a variable separation.

AB - Outer automorphisms of infinite-dimensional representations of the Lie algebra sl(2) are used to construct Lax matrices for integrable Hamiltonian systems and discrete integrable mappings. The known results are reproduced, and new integrable systems are constructed. Classical r-matrices corresponding to the Lax representation with the spectral parameter are dynamic. This scheme is advantageous because quantum systems naturally arise in the framework of the classical r-matrix Lax representation and the corresponding quantum mechanical problem admits a variable separation.

UR - http://www.scopus.com/inward/record.url?scp=0033242389&partnerID=8YFLogxK

U2 - 10.1007/BF02557309

DO - 10.1007/BF02557309

M3 - Article

AN - SCOPUS:0033242389

VL - 118

SP - 164

EP - 172

JO - Theoretical and Mathematical Physics (Russian Federation)

JF - Theoretical and Mathematical Physics (Russian Federation)

SN - 0040-5779

IS - 2

ER -