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  • Question regarding the definition of ideal subalgebra of a Lie algebra . . .
    What is the relation between "derivations" and the "derived subalgebra" of a Lie algebra? 1 How can I show a the Cartan subalgebra being abelian implies its adjoint representation on the original Lie algebra completely commutes?
  • definition of $C^*$-subalgebra - Mathematics Stack Exchange
    Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
  • abstract algebra - How to denote that something is a subalgebra . . .
    By far the most common way to denote this is to say "$\mathfrak{h}$ is a subalgebra of $\mathfrak{g}$" (or perhaps "$\mathfrak{h}\subseteq\mathfrak{g}$ is a subalgebra") There is not any common special notation for this
  • Must $k$-subalgebra of $k[x]$ be finitely generated?
    The very obvious question is whether there is a proof that does not use these fancy SAGBI bases I'll write again if I find an answer to that The important thing to know about them is, however, that a SAGBI basis for a subalgebra is a generating set with certain properties well-suited for computations
  • Why is a semisimple Lie-subalgebra of - Mathematics Stack Exchange
    So a maximal rank subalgebra must have a Cartan subalgebra $\mathfrak{c}$ which is also a Cartan subalgebra of $\mathfrak{g}$ Note that this forces $\mathfrak{h}$ to be the span of $\mathfrak{c}$ together with some of the root spaces In fact these roots must form a subsystem of our original root system
  • What is the definition of subalgebra of given $R$-algebra $A$?
    Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
  • How to find a Cartan subalgebra of $\\mathfrak{so}(n)$?
    To find a Cartan subalgebra for $\mathfrak{su}(n)$ we take advantage that $\mathfrak{su}(n)$ consists of anti-hermitian matrices If a set of elements of $\mathfrak{su}(n)$ commute then they can be simultaneously diagonalized
  • Definition of the subalgebra generated by a set
    Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
  • algebras - Subalgebra Definition - Mathematics Stack Exchange
    If A is an algebra over a field K, and B is a subalgebra, must B be an algebra over K or can it also be an algebra over some subfield of K? For example, if you take $\mathbb{R}$ as an algebra over $\mathbb{R}$, would it be correct to call $\mathbb{Q}$ a subalgebra, since it is an algebra over $\mathbb{Q}$?





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