Wikipedia:WikiProject Mathematics/PlanetMath Exchange/17-XX Nonassociative rings and algebras

17A01 General theory

 * PM: associator, id=6348 -- WP: associator -- Status: A
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: commutator bracket, id=2811 -- WP: commutator -- Status: A
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: nucleus, id=6548 -- WP guess: nucleus -- Status: NC
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: algebras, id=8613new! -- WP guess: algebras -- Status:


 * PM: centralizers in algebra, id=9740new! -- WP guess: centralizers in algebra -- Status:


 * PM: homotopes and isotopes of algebras, id=8614new! -- WP guess: homotopes and isotopes of algebras -- Status:


 * PM: non-associative algebra, id=6845new! -- WP guess: non-associative algebra -- Status:


 * PM: trace forms on algebras, id=8627new! -- WP guess: trace forms on algebras -- Status:

17A05 Power-associative rings

 * PM: power-associative algebra, id=6350 -- WP: power-associative algebra -- Status: A
 * Jtwdog 20:37, 26 September 2005 (UTC)

17A20 Flexible algebras

 * PM: flexible algebra, id=6351 -- WP guess: flexible algebra -- Status: N
 * Jtwdog 20:41, 26 September 2005 (UTC)

17A45 Quadratic algebras (but not quadratic Jordan algebras)

 * PM: quadratic algebra, id=6950new! -- WP guess: quadratic algebra -- Status:

17A75 Composition algebras

 * PM: composition algebra, id=6949new! -- WP guess: composition algebra -- Status:


 * PM: composition algebra over algebaically closed fields, id=9654new! -- WP guess: composition algebra over algebaically closed fields -- Status:


 * PM: composition algebras over \mathbb{Q}, id=9656new! -- WP guess: composition algebras over \mathbbQ -- Status:


 * PM: composition algebras over \mathbb{R}, id=9652new! -- WP guess: composition algebras over \mathbbR -- Status:


 * PM: composition algebras over finite fields, id=9655new! -- WP guess: composition algebras over finite fields -- Status:


 * PM: Hurwitz's theorem on composition algebras, id=9653new! -- WP guess: Hurwitz's theorem on composition algebras -- Status:


 * PM: Jacobson's theorem on composition algebras, id=9651new! -- WP guess: Jacobson's theorem on composition algebras -- Status:


 * PM: octonion, id=7185new! -- WP guess: octonion -- Status:

17A99 Miscellaneous

 * PM: Cayley-Dickson construction, id=6586 -- WP: Cayley-Dickson construction -- Status: A
 * Jtwdog 20:13, 26 September 2005 (UTC)

17B01 Identities, free Lie (super)algebras

 * PM: Lie superalgebra, id=7509new! -- WP guess: Lie superalgebra -- Status:


 * PM: quadratic Lie algebra, id=7379new! -- WP guess: quadratic Lie algebra -- Status:

17B05 Structure theory

 * PM: Killing form, id=3743 -- WP: Killing form -- Status: A
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: Levi's theorem, id=4592 -- WP guess: Levi's theorem -- Status: NC
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: nilradical, id=4594 -- WP: nilradical -- Status: NC
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: radical, id=4593 -- WP: radical -- Status: NC
 * For radical and nilradical, there are already wikipedia for the related notions for associative algebras. I personally, think these should be merged into an article on solvable and nilpotent Lie algebras, which doesn't seem to exist. Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: index of a Lie algebra, id=7380new! -- WP guess: index of a Lie algebra -- Status:


 * PM: regular element of a Lie algebra, id=7382new! -- WP guess: regular element of a Lie algebra -- Status:

17B10 Representations, algebraic theory (weights)

 * PM: adjoint representation, id=2965 -- WP: adjoint representation -- Status: A
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: Ado's theorem, id=3861 -- WP guess: representations of Lie algebras -- Status: NM
 * Jtwdog 21:00, 26 September 2005 (UTC)


 * PM: examples of non-matrix Lie groups, id=3864 -- WP: representations of Lie groups -- Status: NM
 * Alternatively, there could be a page incorporationing Ado's theorem, these examples, and similar things.
 * Jtwdog 21:00, 26 September 2005 (UTC)


 * PM: isotropy representation, id=2992 -- WP guess: isotropy representation -- Status: NC
 * Jtwdog 21:00, 26 September 2005 (UTC)


 * PM: Lie algebra representation, id=2966 -- WP guess: representations of Lie algebras -- Status: NM
 * Jtwdog 21:00, 26 September 2005 (UTC)

17B15 Representations, analytic theory

 * PM: invariant form (Lie algebras), id=3742 -- WP: representations of Lie algebras -- Status: NM
 * Jtwdog 21:01, 26 September 2005 (UTC)

17B20 Simple, semisimple, reductive (super)algebras (roots)

 * PM: Borel subalgebra, id=3666 -- WP: Borel subalgebra -- Status: NM
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: Borel subgroup, id=4035 -- WP guess: Borel subgroup -- Status: NM
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: Cartan matrix, id=3799 -- WP: Cartan matrix -- Status: A
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: Cartan subalgebra, id=3849 -- WP: Cartan subalgebra -- Status: NM
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: Cartan's criterion, id=3744 -- WP guess: Cartan's criterion -- Status: N
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: Casimir operator, id=4624 -- WP: Casimir operator -- Status: NM
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: classification of finite-dimensional representations of semi-simple Lie algebras, id=3653 -- WP: Representations of Lie groups -- Status: NM
 * Jtwdog 20:50, 26 September 2005 (UTC)


 * PM: cohomology of semi-simple Lie algebras, id=4591 -- WP: Lie algebra cohomology -- Status: NM
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: Dynkin diagram, id=4037 -- WP: Dynkin diagram -- Status: A
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: nilpotent cone, id=4748 -- WP: nilpotent cone -- Status: C
 * Jtwdog 18:23, 28 October 2005 (UTC)


 * PM: parabolic subgroup, id=4036 -- WP: parabolic subgroup -- Status: NM
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: pictures of Dynkin diagrams, id=4060 -- WP: Dynkin diagram -- Status: A
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: positive root, id=3656 -- WP: positive root -- Status: NM
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: rank (Lie algebra), id=2348 -- WP: Cartan subalgebra -- Status: NM
 * Jtwdog 20:50, 26 September 2005 (UTC)


 * PM: root lattice, id=3659 -- WP: weight (representation theory) -- Status: NM
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: root system, id=3645 -- WP: root system -- Status: A
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: simple and semi-simple Lie algebras, id=3644 -- WP: simple Lie group -- Status: NM
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: simple root, id=3657 -- WP: simple root -- Status: NM
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: Verma module, id=3665 -- WP guess: Verma module -- Status: C
 * Jtwdog 18:24, 28 October 2005 (UTC)


 * PM: weight (Lie algebras), id=3654 -- WP: weight (representation theory) -- Status: NM
 * Jtwdog 20:50, 26 September 2005 (UTC)


 * PM: weight lattice, id=3660 -- WP: weight (representation theory) -- Status: NM
 * Jtwdog 20:50, 26 September 2005 (UTC)


 * PM: Weyl chamber, id=3661 -- WP: Weyl chamber -- Status: A
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: Weyl group, id=3658 -- WP: Weyl group -- Status: NM
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: Weyl's theorem, id=3877 -- WP guess: Weyl's theorem -- Status: N
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: classification of indecomposable root systems, id=7337new! -- WP guess: classification of indecomposable root systems -- Status:


 * PM: root system underlying a semi-simple Lie algebra, id=7338new! -- WP: root system of a semi-simple Lie algebra -- Status: C
 * MelchiorG (talk) 15:02, 7 February 2010 (UTC)

17B30 Solvable, nilpotent (super)algebras

 * PM: Lie's theorem, id=3860 -- WP guess: Lie's theorem -- Status: C
 * Jtwdog 18:24, 28 October 2005 (UTC)


 * PM: solvable Lie algebra, id=2964 -- WP: Lie algebra -- Status: NM
 * As I said before, I think it's worth just having a separate page on solvable and nilpotent Lie algebras which covers all this business. Jtwdog 20:13, 26 September 2005 (UTC)

17B35 Universal enveloping (super)algebras

 * PM: PoincarÃ©-Birkhoff-Witt theorem, id=3467 -- WP: Poincaré-Birkhoff-Witt theorem -- Status: A
 * Something should be done about correctly copying over é (or maybe it's not worth it). Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: universal enveloping algebra, id=3466 -- WP: universal enveloping algebra -- Status: A
 * Jtwdog 20:13, 26 September 2005 (UTC)

17B56 Cohomology of Lie (super)algebras

 * PM: Lie algebra cohomology, id=4589 -- WP: Lie algebra cohomology -- Status: NM
 * Jtwdog 20:13, 26 September 2005 (UTC)

17B67 Kac-Moody (super)algebras (structure and representation theory)

 * PM: generalized Cartan matrix, id=4625 -- WP: generalized Cartan matrix -- Status: A
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: Kac-Moody algebra, id=4124 -- WP: Kac-Moody algebra -- Status: A
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: extended Cartan matrix, id=7363new! -- WP guess: extended Cartan matrix -- Status:

17B99 Miscellaneous

 * PM: Jacobi identity interpretations, id=3468 -- WP: Jacobi identity -- Status: NM
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: Lie algebra, id=1113 -- WP: Lie algebra -- Status: A
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: local Nagano theorem, id=6464 -- WP guess: local Nagano theorem -- Status: N
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: real form, id=3931 -- WP: real form -- Status: NM
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: Heisenberg algebra, id=7259new! -- WP guess: Heisenberg algebra -- Status:


 * PM: Lie algebras from other algebras, id=8825new! -- WP guess: Lie algebras from other algebras -- Status:


 * PM: modular theory, id=8601new! -- WP guess: modular theory -- Status:


 * PM: restricted Lie algebra, id=8602new! -- WP guess: restricted Lie algebra -- Status:

17C05 Identities and free Jordan structures

 * PM: Jordan algebra, id=6547 -- WP: Jordan algebra -- Status: A
 * Jtwdog 20:13, 26 September 2005 (UTC)


 * PM: Jordan triple product, id=8615new! -- WP guess: Jordan triple product -- Status:


 * PM: quadratic Jordan algebra, id=8626new! -- WP guess: quadratic Jordan algebra -- Status:

17D05 Alternative rings

 * PM: alternative algebra, id=6349 -- WP: alternative algebra -- Status: NM
 * Jtwdog 20:13, 26 September 2005 (UTC)