List of algebras

[blefloch]

List of algebras:

• (super)Lie algebras
• Galilean conformal algebra
• Kac-Moody algebras
• Weyl algebra
• Heisenberg algebra
• parafermionic algebras
• 2d superconformal algebras (http://arxiv.org/abs/hep-th/9203045, http://arxiv.org/abs/hep-th/9703021)
• higher Lie algebra
• (super) W algebras (see http://arxiv.org/abs/math-ph/0408061 and http://arxiv.org/abs/math-ph/0304011 and http://arxiv.org/abs/hep-th/9211094 and http://arxiv.org/abs/hep-th/9111062 and the 92 Toda review I like? and incomplete http://arxiv.org/abs/hep-th/9302124) also Winfinity and W{1+infinity} also real forms http://arxiv.org/abs/hep-th/9802201 also linear realizations http://arxiv.org/abs/0902.0498
• SW(3/2,2) kind of superVirasoro (http://arxiv.org/abs/hep-th/0101116)
• division algebras (R, C, H, O) and relation to spinors (http://arxiv.org/abs/hep-th/0302113 or maybe some Baez papers)
• Manin triples, Drinfeld doubles
• Quantum groups, Uq(slN)
• Poisson-Lie groups (and algebras?)
• vertex algebras, chiral algebras, factorization algebras?
• blob algebra, Temperley--Lieb algebra
• Nichols algebras
• M-theory algebra: is it osp(1|32) or...? According to http://arxiv.org/abs/0711.3498 (and probably others), M-theory algebra is actually E11. Mention of K27 algebra. See https://golem.ph.utexas.edu/category/2014/11/integral_octonions_part_7.html for Baez + Egan discussing it. Maybe http://arxiv.org/abs/hep-th/0511009 is worth looking at. http://arxiv.org/abs/hep-th/0301017 explains some basics about representations of E10 and E11. Maybe http://arxiv.org/abs/hep-th/0212201.
• Courant Lie 2-algebroid (e.g. TM\oplus T^*M for a manifold M).

[blefloch]

• cluster algebras: see Fomin and Zelevinsky's "Cluster algebras" series: I, II, III (also with Berenstein), IV". Also, a talk and a whole webpage of applications.