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Results tagged with ra.rings-and-algebras
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user 124549
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.
5
votes
1
answer
267
views
Categorical Morita equivalence implies equivalence of module categories?
Classically, two rings $R$ and $S$ are Morita equivalent if and only if any of the following is true
($R$-Mod) $\simeq$ ($S$-Mod).
$S \simeq Hom_R(M,M)$, where $M$ is a finitely generated projective …
- 5,230
4
votes
1
answer
173
views
Group representation with algebra structure
I haven't seen this question in standard textbooks, so I decide to give it a try here. It might relate to deeper structures of certain TQFTs, but I'm not sure.
Let $G$ be a finite group. Its finite-di …
- 5,230
4
votes
0
answers
186
views
Cohomology and higher structures
Classically, cohomologies of Lie groups/algebras parametrize extensions. To be precise, given an linear $G$-action on $M$, there is an bijection between $H^2(G;M)$ and the set of extension $E$ of $G$ …
- 5,230
3
votes
Relationship between the Witt algebra and vector fields on the circle
The following answers Question 2 and 3:
For 2, $\frak{g}$ is a dense Lie subalgebra of Vect($S^1$). Tensoring with $\mathbb{C}$ gives you 3.
Identify an infinitestimal diffeomorphism on the cir …
- 5,230
1
vote
2
answers
240
views
Link invariants from Hecke relations of higher order
Alexander theorem says oriented links in $\mathbb{R}^3$ can be
represented by closures of braids. Markov theorem says that
braids related by Markov moves produce isotopic braid closures,
and vice vers …
- 5,230