arXiv:hep-th/9208077v3 21 Mar 1993 BONN–HE–92–24 US–FT–8/92 KUL–TF–92/32 hep-th/9208077 August 1992 The Topography of W ∞ -type Algebras Jos´ e M. Figueroa-O’Farrill 1 ♭ , Javier Mas 2♮ , and Eduardo Ramos 3 ♯ 1 Physikalisches Institut der Universit¨ at Bonn, Nußallee 12, W-5300 Bonn 1, GERMANY 2 Departamento de F´ ısica de Part´ ıculas Elementales, Universidad de Santiago, E-15706 Santiago de Compostela, SPAIN 3 Instituut voor Theoretische Fysica, Universiteit Leuven, Celest¨ ynenlaan 200D, B-3001 Heverlee, BELGIUM ABSTRACT We chart out the landscape of W ∞ -type algebras using W (q) KP —a recently dis- covered one-parameter deformation of W KP . We relate all hitherto known W ∞ -type algebras to W (q) KP and its reductions, contractions, and/or trunca- tions at special values of the parameter. ♭ e-mail: figueroa@pib1.physik.uni-bonn.de ♮ e-mail: jamas@gaes.usc.es ♯ e-mail: fgbda06@blekul11.bitnet (Address after October 1992: Queen Mary and Westfield College, UK)