(Again, I am sorry for the simplicity of these questions. I am a mechanical engineer learning this stuff late in life.)(adsbygoogle = window.adsbygoogle || []).push({});

I have read the following terms or phrases:

group

algebra

group algebra

the algebra of a group

an algebra group

an algebraic group

a group of algebras

So.... could someone please explain this to me?

I understand the stand-alone definitions. But this mixing of terms completely baffles me.

Could some one please take a moment to give a coherent and stand-alone definition of each of these things... You can go easy on the math -- I am slowly getting it (I think): I have an understanding of groups, rings, fields, etc. I am as interested in the syntax of how these words are used.

Are they nouns or adjectives or adverbs? Yes, that is the level of my confusion.

Is algebra a "discipline of math" or " a "thing" or a "class of things."

Here is an example: I have read: Lie algebras are closely related to Lie Groups

(Again, I am sorry: I KNOW these are stupid questions.)

I can say a Macintosh and a Golden Delicious are closely related because they are both apples.

I can say a computer and a desk are closely related because they are both things.

But I cannot say that GREEN and LOVE are related: they are different things.

So what is it in the definition of groups and algebras that can be related?

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# Group algebra terms or phrases

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