About: Semi-invariant of a quiver

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In mathematics, given a quiver Q with set of vertices Q0 and set of arrows Q1, a representation of Q assigns a vector space Vi to each vertex and a linear map V(α): V(s(α)) → V(t(α)) to each arrow α, where s(α), t(α) are, respectively, the starting and the ending vertices of α. Given an element d ∈ Q0, the set of representations of Q with dim Vi = d(i) for each i has a vector space structure.

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  • In mathematics, given a quiver Q with set of vertices Q0 and set of arrows Q1, a representation of Q assigns a vector space Vi to each vertex and a linear map V(α): V(s(α)) → V(t(α)) to each arrow α, where s(α), t(α) are, respectively, the starting and the ending vertices of α. Given an element d ∈ Q0, the set of representations of Q with dim Vi = d(i) for each i has a vector space structure. It is naturally endowed with an action of the algebraic group Πi∈Q0 GL(d(i)) by simultaneous base change. Such action induces one on the ring of functions. The ones which are invariants up to a character of the group are called semi-invariants. They form a ring whose structure reflects representation-theoretical properties of the quiver. (en)
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  • In mathematics, given a quiver Q with set of vertices Q0 and set of arrows Q1, a representation of Q assigns a vector space Vi to each vertex and a linear map V(α): V(s(α)) → V(t(α)) to each arrow α, where s(α), t(α) are, respectively, the starting and the ending vertices of α. Given an element d ∈ Q0, the set of representations of Q with dim Vi = d(i) for each i has a vector space structure. (en)
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  • Semi-invariant of a quiver (en)
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