All Questions
Tagged with deformation-theory differential-graded-algebras
9 questions
3
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Natural transformation and Hochschild cohomology
I am reading the lecture note by Căldăraru:https://arxiv.org/pdf/math/0501094, in the last chapter of this note, he said that we should consider dg category instead of the derived category of coherent ...
- 395
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What is the DGLA controlling deformations of a group representation?
Fix a (discrete) group $G$, characteristic zero field $k$ and representation $\rho_0: G \to \mathrm{GL}_n(k)$. I want to consider the formal deformations of $\rho_0$.
My understanding is there is a ...
- 61
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Is any deformation of an acyclic complex gauge equivalent to a trivial one?
This question is related to this question. Let $(C^{\bullet},d)$ be a cochain complex over a field $k$ with char$k$=0. We fix an Artin local $k$-algebra $(A,m)$. A deformation of $d$ is a new operator ...
- 9,019
6
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Does homotopy equivalence between deformations of cochain complexes imply gauge equivalence?
Let $(C^{\bullet},d)$ be a cochain complex over a field $k$ with char$k$=0. We fix an Artin local $k$-algebra $(A,m)$. A deformation of $d$ is a new operator $d+\epsilon: C^{\bullet}\otimes_k m\to C^{\...
- 9,019
5
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0
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DGLA related to the deformation of hopf Algebras
Recently I was considering Hopf algebras and Drinfeld's twists. I stumbled upon
a certain DGLA one can associate to a Hopf algebra (unital bialgebras actually) by copying the formulas obtained by ...
- 397
7
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2
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Higher commutators in E_n algebras and the Maurer--Cartan equation
Let $A$ be an associative algebra in $dgVect_k$. Then the commutator $[\cdot,\cdot]:A\otimes A\to A$ defined by $[x,y]=xy-(-1)^{|x||y|}yx$ gives $A$ the structure of a (dg-)Lie algebra. The Maurer--...
- 18.7k
7
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How to define the equivalence of Maurer-Cartan elements in an $L_{\infty}$-algebra?
First let $L^{\bullet}$ be a pro-nilpotent differential graded Lie algebra (dgla). We have the set of Maurer-Cartan elements in $L^{\bullet}$ ($MC(L^{\bullet})$) which are $\alpha \in L^1$ such that ...
- 9,019
39
votes
9
answers
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What is a deformation of a category?
I have several naive and possibly stupid questions about deformations of categories. I hope that someone can at least point me to some appropriate references.
What is a deformation of a (linear, dg, ...
- 21k
38
votes
6
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Deformation theory and differential graded Lie algebras
There is supposed to be a philosophy that, at least over a field of characteristic zero, every "deformation problem" is somehow "governed" or "controlled" by a differential graded Lie algebra. See for ...
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