Wikipedia:WikiProject Mathematics/PlanetMath Exchange/17-XX Nonassociative rings and algebras
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.
- If you copy or merge an article from PlanetMath, please update the WP and Status fields for that entry.
- If you have any comments, for example, thoughts on how the PlanetMath article compares to the corresponding Wikipedia article(s), please place such comments on a new indented line following the entry. Comments of this kind are very valuable.
Don't forget to include the relevant template if you copy over text or feel like an external link is warranted
- {{planetmath|id=|title=}} for copied over text
- {{planetmath reference|id=|title=}} for an external link
See the main page for examples and usage criteria.
One can use the web-based program Pmform to convert PlanetMath articles to the Wikipedia format. As a side benefit, this tool will place the PlanetMath template for you.
17-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
edit17-08 Computational methods
edit17A01 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
edit17A45 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
edit17B01 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.)
edit17B67 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
edit17B99 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
edit17C05 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)
edit17D05 Alternative rings
edit- PM: alternative algebra, id=6349 -- WP: alternative algebra -- Status: NM