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Results tagged with noncommutative-algebra
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user 496277
Non-commutative rings and algebras, non-associative algebras. Can be used in combination with ra.rings-and-algebras
9
votes
1
answer
232
views
Formal smoothness of path algebras and connections
Let $k$ be a field of characteristic zero and $A = kQ$ the path algebra associated with a quiver $Q$. The algebra $A$ is said to be formally smooth over $k$ if
$$
\Omega^1_kA = \operatorname{Ker}(\mat …
- 985
3
votes
0
answers
125
views
Trace map on Ext group
Let $R$ be a (possibly non-commutative) unital ring and $M$ be a perfect left $R$-module. Then, we have the trace map
$$
\operatorname{Tr}\colon \mathrm{Hom}_R(M,M)\to R/[R,R]\,.
$$
According to the a …
- 985
5
votes
0
answers
275
views
Representation functor on modules
Let $k$ be a field and $A$ a unital associative $k$-algebra.
The representation functor associates, to each object in non-commutative geometry, a genuine geometric object on the representation variety …
- 985