Wikipedia:WikiProject Mathematics/PlanetMath Exchange/17-XX Nonassociative rings and algebras
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This page provides a list of all articles available at PlanetMath in the following topic:
- 17-XX Nonassociative rings and algebras.
This list will be periodically updated. Each entry in the list has three fields:
- PM : The first field is the link to the PlanetMath article, along with the article's object ID.
- WP : The second field is either a "guessed" link to a correspondingly named Wikipedia article, produced by the script which generated the list, or one or more manually entered links to the corresponding Wikipedia articles on the subject.
- Status : The third field is the status field, which explains the current status of the entry. The recommended status entries are:
Status | means PM article |
N | not needed |
A | adequately covered |
C | copied |
M | merged |
NC | needs copying |
NM | needs merging |
- Please update the WP and Status fields as appropriate.
- if the WP field is correct please remove the qualifier "guess".
- If the corresponding Wikipedia article exists, but the link to it is wrong, please fix the link.
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17-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
[edit]17-08 Computational methods
[edit]17A01 General theory
[edit]- PM: associator, id=6348 -- WP: associator -- Status: A
- PM: commutator bracket, id=2811 -- WP: commutator -- Status: A
- 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
[edit]- PM: power-associative algebra, id=6350 -- WP: power-associative algebra -- Status: A
17A20 Flexible algebras
[edit]- PM: flexible algebra, id=6351 -- WP guess: flexible algebra -- Status: N
17A36 Automorphisms, derivations, other operators
[edit]17A45 Quadratic algebras (but not quadratic Jordan algebras)
[edit]- PM: quadratic algebra, id=6950new! -- WP guess: quadratic algebra -- Status:
17A75 Composition algebras
[edit]- 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:
17A99 Miscellaneous
[edit]- PM: Cayley-Dickson construction, id=6586 -- WP: Cayley-Dickson construction -- Status: A
17Axx General nonassociative rings
[edit]17B01 Identities, free Lie (super)algebras
[edit]- 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
[edit]- PM: Killing form, id=3743 -- WP: Killing form -- Status: A
- PM: Levi's theorem, id=4592 -- WP guess: Levi's theorem -- Status: NC
- PM: nilradical, id=4594 -- WP: nilradical -- 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)
[edit]- PM: adjoint representation, id=2965 -- WP: adjoint representation -- Status: A
- PM: Ado's theorem, id=3861 -- WP guess: representations of Lie algebras -- Status: NM
- 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.
- PM: isotropy representation, id=2992 -- WP guess: isotropy representation -- Status: NC
- PM: Lie algebra representation, id=2966 -- WP guess: representations of Lie algebras -- Status: NM
17B15 Representations, analytic theory
[edit]- PM: invariant form (Lie algebras), id=3742 -- WP: representations of Lie algebras -- Status: NM
17B20 Simple, semisimple, reductive (super)algebras (roots)
[edit]- PM: Borel subalgebra, id=3666 -- WP: Borel subalgebra -- Status: NM
- PM: Borel subgroup, id=4035 -- WP guess: Borel subgroup -- Status: NM
- PM: Cartan matrix, id=3799 -- WP: Cartan matrix -- Status: A
- PM: Cartan subalgebra, id=3849 -- WP: Cartan subalgebra -- Status: NM
- PM: Cartan's criterion, id=3744 -- WP guess: Cartan's criterion -- Status: N
- PM: Casimir operator, id=4624 -- WP: Casimir operator -- Status: NM
- PM: classification of finite-dimensional representations of semi-simple Lie algebras, id=3653 -- WP: Representations of Lie groups -- Status: NM
- PM: cohomology of semi-simple Lie algebras, id=4591 -- WP: Lie algebra cohomology -- Status: NM
- PM: Dynkin diagram, id=4037 -- WP: Dynkin diagram -- Status: A
- PM: nilpotent cone, id=4748 -- WP: nilpotent cone -- Status: C
- PM: parabolic subgroup, id=4036 -- WP: parabolic subgroup -- Status: NM
- PM: pictures of Dynkin diagrams, id=4060 -- WP: Dynkin diagram -- Status: A
- PM: positive root, id=3656 -- WP: positive root -- Status: NM
- PM: rank (Lie algebra), id=2348 -- WP: Cartan subalgebra -- Status: NM
- PM: root lattice, id=3659 -- WP: weight (representation theory) -- Status: NM
- PM: root system, id=3645 -- WP: root system -- Status: A
- PM: simple and semi-simple Lie algebras, id=3644 -- WP: simple Lie group -- Status: NM
- PM: simple root, id=3657 -- WP: simple root -- Status: NM
- PM: Verma module, id=3665 -- WP guess: Verma module -- Status: C
- PM: weight (Lie algebras), id=3654 -- WP: weight (representation theory) -- Status: NM
- PM: weight lattice, id=3660 -- WP: weight (representation theory) -- Status: NM
- PM: Weyl chamber, id=3661 -- WP: Weyl chamber -- Status: A
- PM: Weyl group, id=3658 -- WP: Weyl group -- Status: NM
- PM: Weyl's theorem, id=3877 -- WP guess: Weyl's theorem -- Status: N
- 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
17B30 Solvable, nilpotent (super)algebras
[edit]- PM: Lie's theorem, id=3860 -- WP guess: Lie's theorem -- Status: C
- 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
[edit]- PM: Poincaré-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
17B56 Cohomology of Lie (super)algebras
[edit]- PM: Lie algebra cohomology, id=4589 -- WP: Lie algebra cohomology -- Status: NM
17B60 Lie (super)algebras associated with other structures (associative, Jordan, etc.)
[edit]17B67 Kac-Moody (super)algebras (structure and representation theory)
[edit]- PM: generalized Cartan matrix, id=4625 -- WP: generalized Cartan matrix -- Status: A
- PM: Kac-Moody algebra, id=4124 -- WP: Kac-Moody algebra -- Status: A
- PM: extended Cartan matrix, id=7363new! -- WP guess: extended Cartan matrix -- Status:
17B70 Graded Lie (super)algebras
[edit]17B99 Miscellaneous
[edit]- PM: Jacobi identity interpretations, id=3468 -- WP: Jacobi identity -- Status: NM
- PM: Lie algebra, id=1113 -- WP: Lie algebra -- Status: A
- PM: local Nagano theorem, id=6464 -- WP guess: local Nagano theorem -- Status: N
- 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:
17Bxx Lie algebras and Lie superalgebras
[edit]17C05 Identities and free Jordan structures
[edit]- PM: Jordan algebra, id=6547 -- WP: Jordan algebra -- Status: A
- PM: Jordan triple product, id=8615new! -- WP guess: Jordan triple product -- Status:
- PM: quadratic Jordan algebra, id=8626new! -- WP guess: quadratic Jordan algebra -- Status:
17Cxx Jordan algebras (algebras, triples and pairs)
[edit]17D05 Alternative rings
[edit]- PM: alternative algebra, id=6349 -- WP: alternative algebra -- Status: NM