Questions tagged [bimodules]
The bimodules tag has no usage guidance.
22
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Gerstenhaber bracket for Hochschild cohomology with values in a module
I am currently trying to compute obstructions in a Hochschild cohomology $\mathrm{HH}^* (A,M)$ where $A$ is a $\Bbbk$-algebra and $M$ an $A$-bimodule. The obstruction I am looking at looks a lot like ...
- 203
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1
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Are algebras with invertible linear duals always Frobenius?
Let $A$ be a finite dimensional algebra over a ground field $k$. The linear dual $A^* = Hom_k(A,k)$ is naturally an $A$-$A$ bimodule. I am interested in those algebras such that $A^*$ is an invertible ...
- 26.7k
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68
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MAGMA-question concerning dual modules of bimodules
Let $G$ be a finite group and let $H_1,H_2\leq G$.
Let char$(k)=p>0$, $k$ a field, large enough.
Let $T$ be a $(kH_1, kH_2)$-bimodule given in MAGMA.
Moreover, let $T$ be finitely generated ...
- 1,655
1
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2
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407
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A description of the kernel of projection map from the tensor algebra to the symmetric algebra $T(V)\to S(V)$
Let $V$ be a vector space over some arbitrary field. Let $T(V)$ and $S(V)$ be the tensor and symmetric algebras over $V$. We have the projection map $T(V)\to S(V)$, given by $x_1\otimes\cdots\otimes ...
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Dual of a bimodule
For a noncommutative ring $R$, and an $R$-$R$-bimodule $B$, is there a "correct/natural" notion of a dual bimodule? I am interested, really, when $B$ is projective as a left $R$-module.
Note: ...
6
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1
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219
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"Left Brace Module"
Let $A$ be an algebra over the brace tree operad and $M$ a module over some base ring.
Is there a good notion of a "left brace module" over a brace algebra?
I do not think the definition of a module ...
- 507
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152
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Characterizing fullness of a von Neumann algebra by the topology of its bimodules
Let $\mathcal{M}$ be a $\mathrm{II}_1$ factor. Among other characterizations, it is said to be full iff the adjoint map:
$$
\mathrm{Ad}: U(\mathcal{M})/\mathbb{T} \longrightarrow \mathrm{Aut}(\...
- 1,070
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Is there an established name for bi-module morphisms that swap the module structures?
Let $P,Q$ denote two $R$-bimodules where $R$ is a ring, for my purposes commutative. I'll write the left $R$-module structure by multiplication on the left and analogously for the right structure.
...
- 5,213
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Decomposition of Banach bimodules of Banach algebras
Let $A$ and $B$ be Banach algebras, $\theta:A\rightarrow \mathbb{C}$ be a character (i.e., a multiplicative linear functional) and $A\oplus _{\theta} B$ be the $l^1$-direct sum of $A$ and $B$ equipped ...
- 167
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Slick construction of Hochschild complex
Let $R$ be a $k$-algebra and $M$ be an $(R,R)$-bimodule. Let $[n] \mapsto M \otimes R^{\otimes n}$ be the simplicial $k$-module which defines the Hochschild homology $H_*(R,M)$. Is it possible to ...
- 5,364
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58
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Comparing right and left quasi-representable bimodules
Let $\mathcal V$ be your favourite (closed, symmetric) monoidal model category. To fix ideas, set $\mathcal V = \mathrm{Ch}(k)$, the category of chain complexes over a fixed commutative ring. Given a $...
- 2,019
5
votes
1
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249
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When are countably generated Hilbert modules generated by c.p.c. order zero maps?
Throughout let $B$ be a stable C*-algebra, i.e. $B\cong B\otimes K$, where $K$ is the C*-algebra of compact operators on an infinite dimensional separable Hilbert space. It is well-known that any ...
- 417
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Does this kind of non-noetherian bimodule exist?
Question: Do there exist simple rings $R$ and $S$ (i.e., rings with no proper nonzero ideals) and an $(R,S)$-bimodule $M$ such that
$M$ is finitely generated both as a left $R$-module and a right
$...
- 4,977
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When were bordered Heegaard Floer homology's DA bimodules invented?
This is less of a strictly mathematical question and more of a reference request.
In their paper "Bordered Heegaard Floer Homology (http://arxiv.org/pdf/0810.0687.pdf)," Lipshitz-Ozsvath-Thurston (...
- 1,444
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1k
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Strong Morita Equivalence and Morphisms Between $ C^{*} $-Algebras
If $ A $ and $ B $ are $ C^{*} $-algebras, then they are strongly Morita equivalent if there exist a $ (B,A) $-bimodule $ E $ and an $ (A,B) $-bimodule $ F $ such that
$$
E \otimes_{A} F \cong B \quad ...
- 723
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Morphisms between $K_0$
I suppose this is a question with a well known answer. Suppose $A$ and $B$ are two algebras over some field and there is a map
$$
f: \operatorname{K_0}(A) \to \operatorname{K_0}(B)
$$
is it ...
- 1,525
3
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1
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Bimodule version of IBN
Hello all,
Does anyone have an example in mind of a ring $R$ for which $R^n\cong R^m$ as $R,R$ bimodules for some positive integers $n\neq m$?
I would be a little surprised if someone showed no such ...
- 1,458
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1k
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Intrinsic characterization of Soergel bimodules?
A Soergel bimodule (for $S_n$) is a bimodule over $R = \mathbb{Q}[x_1,\dots,x_n]$ which appears as a summand/grading shift of tensor products of the basic bimodules
$$B_{i,i+1} = R \otimes_{i,i+1} R$$
...
- 9,953
18
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2
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Is the endomorphism algebra of a dualizable bimodule necessarily finite dimensional?
Let $k$ be field. Let $A$, $B$ be $k$-algebras, and let ${}_AM_B$ be a dualizable bimodule.
Pre-Question (too naive): Is the algebra of $A$-$B$-bilinear endomorphisms of $M$ necessarily finite ...
- 41.6k
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The growthrate of the homology of $H_*(M^{\otimes_A n})$ for a DG-bimodule $M$
Suppose you have an DG-algebra $A$, and a DG-bimodule $M$ over $A$. Under which conditions will the rank of the bimodules $H_*(M^{\otimes_A n})$ will grow exponentially in terms of $n$? Here $M^{\...
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One-parameter semigroups of bimodules
Suppose M is a von Neumann algebra.
Consider a monoidal category of bimodules over M.
Here a bimodule is a Hilbert space with two normal representations of M.
The monoidal structure is given by Connes'...
- 34.4k
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8
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Bimodules in geometry
Grothendieck's approach to algebraic geometry in particular tells us to treat all rings as rings of functions
on some sort of space. This can also be applied outside of scheme theory (e.g., Gelfand-...
- 34.4k