Representation of Algebras is the branch of abstract algebra that studies modules over an associative $R$-algebra $A$ when $R$ is a commutative ring. One of the basic problems in this field is to classify non isomorphic indecomposable representations of a given $R$-algebra $A$
Questions tagged [representation-of-algebras]
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Character of a module is same as character of some semisimple module
Let $\mathbb{F}$ be a field with $char~\mathbb{F}=0$, $A$ is a finite dimensional $F$-algebra. If $\theta$ is a representation of $A$, define character of $\theta$, to be $\chi_{\theta}(x)=tr~\theta(x)$. Since, two modules are isomorphic as…
user300
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Can the $\mathbb R$-algebra $M_n(\mathbb C)$ be generated using a set of only $2n$ of its elements?
Can the $\mathbb R$-algebra $M_n(\mathbb C)$ be generated using a set of only $2n$ of its elements?
My thoughts are that $M_n(\mathbb C)$ is a simple ring, and we are asking whether there is a surjective $\mathbb R$-algebra homomorphism…
wlad
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$A$ is an associative algebra and $V$ is a representation. Then $\operatorname{End}_{A}(A)=A^{op}?$ (exercise from notes by Etingof)
Let $A$ be an associative algebra. If $V$ is a representation of $A$, write $\operatorname{End}_A(V)$ to denotes the algebra of all homomorphisms of representations $V \to V$ . Show that $\operatorname{End}_A(A) = A^{op}$,the algebra A with opposite…
Lionel666
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