The bimodules tag has no wiki summary.

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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 ...

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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 ...

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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 ...

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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
$$B_{i,i+1} = R \otimes_{i,i+1} R$$
...

**14**

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**2**answers

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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 ...

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votes

**1**answer

138 views

### 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 ...

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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 ...

**12**

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**8**answers

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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., ...