User:Fropuff/Tasklist

• /Spheres
• /Algebras
• write an article on the 3-sphere group = Sp(1) = SU(2). Decide on a good name for this article.
• orientability and orientable manifold should be merged. See also orientation (mathematics). Should we have one page for nonorientable surfaces and another for orientable manifolds, or should the two be discussed in the same article?
• Expand hom-functor
• Lorentz transformation needs to be reworked
• knot polynomial and skein relation need to be cleaned up
• lattice (group) could use some clean-up and additions (e.g. when are two lattices defined by different bases equivalent)
• Möbius transformation needs some clean-up
• work on immersions and embeddings for Klein bottle, Möbius strip, and real projective plane (cross-cap)
• the article on quaternions needs a major cleanup, as does quaternions and spatial rotations; but first finish your article on the unit quaternion group — 17:09, 30 January 2006 (UTC)

• add articles on
  • Lie group homomorphism
  • Lie algebra of a Lie group (discuss in detail the Lie group-Lie algebra correspondence)
  • matrix Lie group and matrix Lie algebra
• work on Maurer-Cartan form
• separate simple Lie algebra from simple Lie group; correct the definition of the latter
• fix the definition of a Lie subgroup to include immersed Lie subgroups
• fix errors in semisimple Lie algebra regarding algebraically closed fields and fields of prime characteristic
• root system should define the root sytem of a simple Lie algebra (the primary example)

• Write articles on
  • supermatrix
  • supermodule
  • super ringed space
  • superscheme
• Expand supermanifold and give a rigorous definition. Mention alternatives.
• Elaborate on Berezin integral.
• Move supergroup (physics) to Lie supergroup, correct the definition and expand.
• Rewrite Lie superalgebra. Give more examples.
• Write articles on the simple Lie superalgebras and groups (unitary, orthosymplectic, and strange)

Stubs needing attention:

affine Lie algebra -- current algebra -- join (topology) -- matrix ring -- nonlinear sigma model -- spin group -- subbundle --

Redirects that should not be:

bifunctor -- knot diagram -- knot sum -- Sp(1) -- SU(2) -- SU(3) --

Red links or articles I'd like to write if I had more time:

Algebra

binary polyhedral group -- Clifford module -- generalized inner product space -- integral octonion -- quaternionic linear group -- supermodule --

Category theory

category of modules -- free category --

Geometry and topology

complex coordinate space -- flat bundle -- flat connection -- flat manifold -- flat torus -- flat vector bundle -- Gosset-Elte polytope -- Klein surface -- Kleinian singularity -- locally contractible space -- octonionic projective line -- octonionic projective plane -- orientation form -- quaternionic coordinate space -- symplectic reduction -- tensor product bundle --

Knot theory

closed braid -- link diagram --

Physics

conformal primary field -- spinor notation -- Verlinde formula --

These pages are works in progress. I may merge them with their respective articles if and when they are completed.