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YCor
YCor
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Are differential forms related to Azumaya Algebrasalgebras?

While studying vector bundle valued differential forms, $\Omega^{\bullet}(M, E)$, or $\Omega^{\bullet}(M, End(E))$$\Omega^{\bullet}(M, \mathrm{End}(E))$ if that helps this discussion, I've come across some work in Azumaya Algebrasalgebras. Thinking of $\Omega$ as an $R$-module, taking values in a bundle, and reading about how Azumaya algebras can be thought of locally being a matrix algebra, in the right context, it seems there should be a connection between $\Omega$ and Azumaya Algebrasalgebras. Can anyone point me in the right direction or tell me why this doesn't work?

Question: Can we say that $\Omega^{\bullet}(M,E)$ is an Azumaya Algebraalgebra?

Are differential forms related to Azumaya Algebras?

While studying vector bundle valued differential forms, $\Omega^{\bullet}(M, E)$, or $\Omega^{\bullet}(M, End(E))$ if that helps this discussion, I've come across some work in Azumaya Algebras. Thinking of $\Omega$ as an $R$-module, taking values in a bundle, and reading about how Azumaya algebras can be thought of locally being a matrix algebra, in the right context, it seems there should be a connection between $\Omega$ and Azumaya Algebras. Can anyone point me in the right direction or tell me why this doesn't work?

Question: Can we say that $\Omega^{\bullet}(M,E)$ is an Azumaya Algebra?

Are differential forms related to Azumaya algebras?

While studying vector bundle valued differential forms, $\Omega^{\bullet}(M, E)$, or $\Omega^{\bullet}(M, \mathrm{End}(E))$ if that helps this discussion, I've come across some work in Azumaya algebras. Thinking of $\Omega$ as an $R$-module, taking values in a bundle, and reading about how Azumaya algebras can be thought of locally being a matrix algebra, in the right context, it seems there should be a connection between $\Omega$ and Azumaya algebras. Can anyone point me in the right direction or tell me why this doesn't work?

Question: Can we say that $\Omega^{\bullet}(M,E)$ is an Azumaya algebra?

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cheyne
cheyne
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While studying vector bundle valued differential forms, $\Omega^{\bullet}(M, E)$, or $\Omega^{\bullet}(M, End(E))$ if that helps this discussion, I've come across some work in Azumaya Algebras. Thinking of $\Omega$ as an $R$-module, taking values in a bundle, and reading about how Azumaya algebras can be thought of locally being a matrix algebra, in the right context, it seems there should be a connection between $\Omega$ and Azumaya Algebras. Can anyone point me in the right direction or tell me why this doesn't work?

Question: Can we say that $\Omega^{\bullet}(M,E)$ is an Azumaya Algebra?

While studying vector bundle valued differential forms, $\Omega^{\bullet}(M, E)$, or $\Omega^{\bullet}(M, End(E))$ if that helps this discussion, I've come across some work in Azumaya Algebras. Thinking of $\Omega$ as an $R$-module, taking values in a bundle, and reading about how Azumaya algebras can be thought of locally being a matrix algebra, in the right context, it seems there should be a connection between $\Omega$ and Azumaya Algebras. Can anyone point me in the right direction or tell me why this doesn't work?

While studying vector bundle valued differential forms, $\Omega^{\bullet}(M, E)$, or $\Omega^{\bullet}(M, End(E))$ if that helps this discussion, I've come across some work in Azumaya Algebras. Thinking of $\Omega$ as an $R$-module, taking values in a bundle, and reading about how Azumaya algebras can be thought of locally being a matrix algebra, in the right context, it seems there should be a connection between $\Omega$ and Azumaya Algebras. Can anyone point me in the right direction or tell me why this doesn't work?

Question: Can we say that $\Omega^{\bullet}(M,E)$ is an Azumaya Algebra?

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cheyne
cheyne
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Are differential forms related to Azumaya Algebras?

While studying vector bundle valued differential forms, $\Omega^{\bullet}(M, E)$, or $\Omega^{\bullet}(M, End(E))$ if that helps this discussion, I've come across some work in Azumaya Algebras. Thinking of $\Omega$ as an $R$-module, taking values in a bundle, and reading about how Azumaya algebras can be thought of locally being a matrix algebra, in the right context, it seems there should be a connection between $\Omega$ and Azumaya Algebras. Can anyone point me in the right direction or tell me why this doesn't work?