12,390 research outputs found

    The Algebras of Large N Matrix Mechanics

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    Extending early work, we formulate the large N matrix mechanics of general bosonic, fermionic and supersymmetric matrix models, including Matrix theory: The Hamiltonian framework of large N matrix mechanics provides a natural setting in which to study the algebras of the large N limit, including (reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We find in particular a broad array of new free algebras which we call symmetric Cuntz algebras, interacting symmetric Cuntz algebras, symmetric Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the role of these algebras in solving the large N theory. Most important, the interacting Cuntz algebras are associated to a set of new (hidden) local quantities which are generically conserved only at large N. A number of other new large N phenomena are also observed, including the intrinsic nonlocality of the (reduced) trace class operators of the theory and a closely related large N field identification phenomenon which is associated to another set (this time nonlocal) of new conserved quantities at large N.Comment: 70 pages, expanded historical remark

    Hilbert C*-modules and related subjects - a guided reference overview I

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    The overview contains 450 references of books, chapters of monographs, papers, preprints and Ph.~D.~thesises which are concerned with the theory and/or various applications of Hilbert C*-modules. To show a way through this amount of literature a four pages guide is added clustering sources around major research problems and research fields, and giving information on the historical background. Two smaller separate parts list references treating Hilbert modules over Hilbert*-algebras and Hilbert modules over (non-self-adjoint) operator algebras. Any additions, corrections and forthcoming information are welcome.Comment: LaTeX 2.09, 23 page

    On the Structure of Monodromy Algebras and Drinfeld Doubles

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    We give a review and some new relations on the structure of the monodromy algebra (also called loop algebra) associated with a quasitriangular Hopf algebra H. It is shown that as an algebra it coincides with the so-called braided group constructed by S. Majid on the dual of H. Gauge transformations act on monodromy algebras via the coadjoint action. Applying a result of Majid, the resulting crossed product is isomorphic to the Drinfeld double D(H). Hence, under the so-called factorizability condition given by N. Reshetikhin and M. Semenov-Tian- Shansky, both algebras are isomorphic to the algbraic tensor product H\otimes H. It is indicated that in this way the results of Alekseev et al. on lattice current algebras are consistent with the theory of more general Hopf spin chains given by K. Szlach\'anyi and the author. In the Appendix the multi-loop algebras L_m of Alekseev and Schomerus [AS] are identified with braided tensor products of monodromy algebras in the sense of Majid, which leads to an explanation of the ``bosonization formula'' of [AS] representing L_m as H\otimes\dots\otimes H.Comment: Latex, 22 p., revised Oct.6, 1996, some references added, more historical background in the introduction, some minor technical improvements, E-mail: [email protected]

    Remarks on Geometric Mechanics

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    This paper gives a few new developments in mechanics, as well as some remarks of a historical nature. To keep the discussion focused, most of the paper is confined to equations of "rigid body", or "hydrodynamic" type on Lie algebras or their duals. In particular, we will develop the variational structure of these equations and will relate it to the standard variational principle of Hamilton
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