Return to Question

In this question a CAU algebra is a commutative associative unital algebra over $\mathbb{C}$.

Let $n\geq 1$ be an integer. There is an obvious family of $n$-dimensional unital algebras parametrized by $\mathbb{C}^{n(n-1)^2}$ such that any $n$-dimensional unital algebra is isomorphic to at least one algebra in the family.

A closed (possibly reducible) subvariety $V\subset \mathbb{C}^{n(n-1)^2}$ is representative if any $n$-dimensional CAU algebra is isomorphic to at least one algebra in the corresponding subfamily.

For $n\leq 6$ there is a zero-dimensional representative subvariety. What can we say about the minimum dimension of a representative subvariety for $n\geq 7$?

Let $n\geq 1$ be an integer. There is an obvious family of $n$-dimensional unital algebras parametrized by $\mathbb{C}^{n(n-1)^2}$ such that any $n$-dimensional unital algebra is isomorphic to at least one algebra in the family.

A closed (possibly reducible) subvariety $V\subset \mathbb{C}^{n(n-1)^2}$ is representative if any $n$-dimensional commutative associative unital algebra is isomorphic to at least one algebra in the corresponding subfamily.

For $n\leq 6$ there is a zero-dimensional representative subvariety. What can we say about the minimum dimension of a representative subvariety for $n\geq 7$?

In this question a CAU algebra is a commutative associative unital algebra over $\mathbb{C}$.

Let $n\geq 1$ be an integer. There is an obvious family of $n$-dimensional CAU algebras parametrized by $\mathbb{C}^{\frac{n^2(n-1)}{2}}$ such that any $n$-dimensional CAU algebra is isomorphic to at least one algebra in the family.

A closed (possibly reducible) subvariety $V\subset \mathbb{C}^{\frac{n^2(n-1)}{2}}$ is representative if any $n$-dimensional CAU algebra is isomorphic to at least one algebra in the corresponding subfamily.

For $n\leq 6$ there is a zero-dimensional representative subvariety. What can we say about the minimum dimension of a representative subvariety for $n\geq 7$?

In this question a CAU algebra is a commutative associative unital algebra over $\mathbb{C}$.

Let $n\geq 1$ be an integer. There is an obvious family of $n$-dimensional unital algebras parametrized by $\mathbb{C}^{n(n-1)^2}$ such that any $n$-dimensional unital algebra is isomorphic to at least one algebra in the family.

A closed (possibly reducible) subvariety $V\subset \mathbb{C}^{n(n-1)^2}$ is representative if any $n$-dimensional CAU algebra is isomorphic to at least one algebra in the corresponding subfamily.

For $n\leq 6$ there is a zero-dimensional representative subvariety. What can we say about the minimum dimension of a representative subvariety for $n\geq 7$?

In this question a CAU algebra is a commutative associative unital algebra over $\mathbb{C}$.

Let $n\geq 1$ be an integer. There is an obvious family of $n$-dimensional CAU algebras parametrized by $\mathbb{C}^{\frac{n(n-1)}{2}}$ such that any $n$-dimensional CAU algebra is isomorphic to at least one algebra in the family.

A closed (possibly reducible) subvariety $V\subset \mathbb{C}^{\frac{n(n-1)}{2}}$ is representative if any $n$-dimensional CAU algebra is isomorphic to at least one algebra in the corresponding subfamily.

For $n\leq 6$ there is a zero-dimensional representative subvariety. What can we say about the minimum dimension of a representative subvariety for $n\geq 7$?

In this question a CAU algebra is a commutative associative unital algebra over $\mathbb{C}$.

Let $n\geq 1$ be an integer. There is an obvious family of $n$-dimensional CAU algebras parametrized by $\mathbb{C}^{\frac{n^2(n-1)}{2}}$ such that any $n$-dimensional CAU algebra is isomorphic to at least one algebra in the family.

A closed (possibly reducible) subvariety $V\subset \mathbb{C}^{\frac{n^2(n-1)}{2}}$ is representative if any $n$-dimensional CAU algebra is isomorphic to at least one algebra in the corresponding subfamily.

For $n\leq 6$ there is a zero-dimensional representative subvariety. What can we say about the minimum dimension of a representative subvariety for $n\geq 7$?