caa a22 4500 469099089 CHVBK 20180323133040.0 cr unu---uuuuu 170328e19920101xx s 000 0 eng 10.1007/BF00430005 doi (NATIONALLICENCE)springer-10.1007/BF00430005 Fronsdal C. Department of Physics, University of California, 90024-1547, Los Angeles, CA, USA aut gl q ( n ) and quantum monodromy [Elektronische Daten] [C. Fronsdal] A generalized Toda lattice based on gl(n) is considered. The Poisson brackets are expressed in terms of a Lax connection, L=∂σ−Φ(σ) and a classical r-matrix, {Φ1,Φ2}=[r,Φ1+Φ2}. The essential point is that the local lattice transfer matrix is taken to be the ordinary exponential, T=eΦ; this assures the intepretation of the local and the global transfer matrices in terms of monodromy, which is not true of the T-matrix used for the sl(n) Toda lattice. To relate this exponential transfer matrix to the more manageable and traditional factorized form, it is necessary to make specific assumptions about the equal time operator product expansions. The simplest possible assumptions lead to an equivalent, factorized expression for T, in terms of operators in (an extension of) the enveloping algebra of gl(n). Restricted to sl(n), and to multiplicity-free representations, these operators satisfy the commutation relations of sl q (n), which provides a very simple injection of sl q (n) into the enveloping algebra of sl(n). A deformed coproduct, similar in form to the familiar coproduct on sl q (n), turns gl(n) into a deformed Hopf algebra gl q (n). It contains sl q (n) as a subalgebra, but not as a sub-Hopf algebra. Kluwer Academic Publishers, 1992 Letters in Mathematical Physics Kluwer Academic Publishers 24/1(1992-01-01), 73-78 0377-9017 24:1<73 1992 24 11005 https://doi.org/10.1007/BF00430005 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00430005 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Fronsdal C. Department of Physics, University of California, 90024-1547, Los Angeles, CA, USA aut NATIONALLICENCE 773 0- Letters in Mathematical Physics Kluwer Academic Publishers 24/1(1992-01-01), 73-78 0377-9017 24:1<73 1992 24 11005 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer