Unanswered Questions
1,113 questions with no upvoted or accepted answers
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What happens to simple modules under Ringel duality?
If $A$ is a quasi-hereditary algebra then its Ringel dual $A'=End_A(T)$ is the endomorphism algebra of a (minimal) full tilting module $T$ for $A$. The algebra $A'$ is again quasi-hereditary, although ...
- 568
11
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What do Multilinear Forms tell us about Representations?
The last few days I have been calculating whether certain group representations are real, complex, or quaternionic. It is well-known that the type of the representation corresponds to what type of ...
- 5,191
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Does Wedderburn's Theorem hold constructively?
Wedderburn's Theorem states that every finite division ring is commutative. Perhaps even more surprising, this implies that every finite reduced ring is commutative. The proofs that I am aware of ...
10
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485
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Reconstruction of commutative differential graded algebras
Let $k$ be an algebraically closed field of characteristic $0$.
Let $A,B$ be commutative differential graded algebras (cdga) over $k$ such that $H^{i}(A)=H^{i}(B) =0 \ (i>0)$.
Here, differentials ...
- 869
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Near-ring spaces
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10
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In search of lost graded rings
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10
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Is $\mathbb{Z}_p \otimes_{\mathbb{Z}} \mathbb{Z}_p$ coherent?
The question is as in the title:
Is the ring $\mathbb{Z}_p \otimes_{\mathbb{Z}} \mathbb{Z}_p = \mathbb{Z}_p \otimes_{\mathbb{Z}_{(p)}} \mathbb{Z}_p$ coherent?
As shown in the related question, the ...
- 2,956
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225
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What is the meaning of the coefficients of the Alekseev-Torossian associator
Drinfeld associators became a central object in mathematics and mathematical physics. They appear in deformation quantization, quantum groups, in the proof of the formality of the little disks operad, ...
- 8,185
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Recover the field from its Milnor K-groups
For every field $F$, consider $K_n^M(F)$ the $n$-th Milnor K-group of $F$ for each $n \in \Bbb N$, and form the Milnor K-ring $K^M(F)=\oplus_{n \geq 0}K^M_n(F)$. For instance, $K_1(F)=F^{\times}$.
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10
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Equational theory in the signature (+,*,0,1) of sedenions and beyond
Consider a Cayley-Dickson algebra $(X,+,∗,0,1)$, that is an algebra generated from the reals by the Cayley-Dickson construction. From complexes to quaternions, we lose commutativity of multiplication, ...
- 2,063
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237
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Generalized eigen property of a matrix
Given a $n \times n$ invertible matrix $A$, I am interested in the set
$$
\mathcal{S}(A) = \{ D \textrm{ diagonal matrix } \mid \det(D - A) = 0 \}.
$$
Thus, for all eigenvalues $\lambda_i$, we have $...
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239
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Has anyone seen this construction of dg algebras?
Let $A$ be an associative algebra, $M$ a right $A$-module. Suppose we are given an $A$-module homomorphism $M \to A$. Then we can make $M$ itself into an associative algebra via the multiplication
$$ ...
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10
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842
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Scholze's infinite to finite type ring theory reductions?
In following essay "The Perfectoid Concept: Test Case for an Absent Theory" by Michael Harris, there is the following sentence I found to be quite striking.
The most virtuosic pages in Scholze's ...
- 1,429
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394
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Lazard's theorem and Hopf structures on the polynomial algebra
Let $k$ be an algebraically closed field of characteristic $0$. A well-known result of Lazard's states that an algebraic group which is isomorphic as a variety to an affine space is unipotent (M. ...
CommunityBot
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10
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Are local finite dimensional Hopf algebras symmetric?
Recall that a finite dimensional algebra $A$ over a field $K$is called a Frobenius algebra in case $A \cong D(A)$ as right modules, where $D(A) \cong Hom_K(A,K)$. In case $A \cong D(A)$ as bimodules, ...
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