According to Wikipedia, for a given group $G$, the relation of its subgroup $H$ to $G$ is usually denoted by $H\le G$ (or $H\lt G$ for a proper subgroup).
What about algebras? What is the most common/usual/accepted way of denoting that $\mathfrak h$ is a subalgebra of $\mathfrak g$?
Examples I have encountered:
- $\mathfrak h-\mathfrak g$
- $\mathfrak h\,\backslash\, \mathfrak g$
- $\mathfrak h\le \mathfrak g$
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.
(I would also disagree that subgroups are "usually" denoted with $H\leq G$. This notation is sometimes used and is widely recognized, but again it is very common to not use any special symbol for this and just write it in words.)