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Results tagged with ra.rings-and-algebras
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user 32389
Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.
14
votes
Accepted
Rings satisfying the polynomial equation $x^4=x^2$
Alfred Foster introduced a notion of Boolean-like ring in a 1946 paper http://www.ams.org/tran/1946-059-01/S0002-9947-1946-0015045-5/S0002-9947-1946-0015045-5.pdf He calls elements of a ring that sat …
- 16.5k
1
vote
Is there a "conceptual" proof that an Albert algebra is a Jordan algbera?
Why 3×3 Hermitian matrices over an octonion algebra form a Jordan algebra and what means its exceptionality is explained in a very nice book by Kevin McCrimmon "A taste of Jordan algebras" http://www …
- 16.5k
8
votes
List of Casimir elements of low dimensional Lie algebras
A more general problem (finding all invariant functions of the group generators for all real Lie algebras of dimension up to five) was considered in Invariants of real low dimension Lie algebras by J. …
- 16.5k
7
votes
Applications of Jordan algebras
Jordan algebras were originally introduced by Pascual Jordan in a hope to generalize the orthodox formulation of quantum mechanics, but this program was not successful as far as the generalization of …
- 16.5k
2
votes
What are the simple Lie superalgebras of type E?
I think Kac - Lie superalgebras is a useful reference.
Exceptional Lie superalgebras G(3) and F(4) can indeed be expressed in terms of octonions:
Sudbery - Octonionic description of exceptional Lie s …
- 16.5k
2
votes
Graph of a Lie super algebra
A good review article on Lie superalgebras by V.G. Kac can be found here:
https://www.sciencedirect.com/science/article/pii/0001870877900172
Certain subtle points about Cartan matrices and Dynkin di …
- 16.5k
24
votes
Origin of exact sequences
In the book "A History of Algebraic and Differential Topology, 1900 - 1960" by
Jean Dieudonne http://www.amazon.com/History-Algebraic-Differential-Topology-1900/dp/0817649069 there is a section "Exac …
- 16.5k