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1. • CommentRowNumber1.
   • CommentAuthorzskoda
   • CommentTimeJun 29th 2024
   • PermaLink
   Author: zskoda
   Format: MarkdownItexJust a stub explaining the ramifications of common usages of the (rather undefined) term. <a href="https://ncatlab.org/nlab/revision/quantum+algebra/1">v1</a>, <a href="https://ncatlab.org/nlab/show/quantum+algebra">current</a>

   Just a stub explaining the ramifications of common usages of the (rather undefined) term.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJun 29th 2024
   • (edited Jun 29th 2024)
   • PermaLink
   Author: Urs
   Format: MarkdownItexBrush-up. $\,$ Fixed the grammar. (NB: It is not the case that "a quantum algebra is a synonym" -- if that were the case it would be called a *quantum synonym* instead ;-) $\,$ Then I don't understand this paragraph: > Large [[noncommutative algebras]] (say free associative algebras and alike) are typically not called quantum. Nevertheless, few authors view any noncommutative associative algebra as quantum. The use of "nevertheles" here seems illogical. The second sentence seems to instead strengthen the standpoint of the first one, in which case it would make sense to instead say "In fact" or "Moreover". $\,$ You could try to copy and paste the usual pre-amble, it's not hard: +-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ###Context### #### Algebra +--{: .hide} [[!include higher algebra - contents]] =-- =-- =-- \tableofcontents <a href="https://ncatlab.org/nlab/revision/diff/quantum+algebra/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/quantum+algebra/2">v2</a>, <a href="https://ncatlab.org/nlab/show/quantum+algebra">current</a>

   Brush-up.

   $\,$

   Fixed the grammar. (NB: It is not the case that “a quantum algebra is a synonym” – if that were the case it would be called a quantum synonym instead ;-)

   $\,$

   Then I don’t understand this paragraph:

   Large noncommutative algebras (say free associative algebras and alike) are typically not called quantum. Nevertheless, few authors view any noncommutative associative algebra as quantum.

   The use of “nevertheles” here seems illogical. The second sentence seems to instead strengthen the standpoint of the first one, in which case it would make sense to instead say “In fact” or “Moreover”.

   $\,$

   You could try to copy and paste the usual pre-amble, it’s not hard:

     +-- {: .rightHandSide}
     +-- {: .toc .clickDown tabindex="0"}
     ###Context###
     #### Algebra
     +--{: .hide}
     [[!include higher algebra - contents]]
     =-- 
     =--
     =--
   
    \tableofcontents
   

   diff, v2, current

3. • CommentRowNumber3.
   • CommentAuthorzskoda
   • CommentTimeJun 29th 2024
   • PermaLink
   Author: zskoda
   Format: MarkdownItex> Large noncommutative algebras (say free associative algebras and alike) are typically not called quantum. Nevertheless, few authors view any noncommutative associative algebra as quantum. I do not understand where is a confusion. I see the two sentences as about quite the unlike usages of the term. Few/a few means in my understanding not many/only several. While for most people quantum is close to commutative (q-deformations, Noetherian, finite Gelfand-Kirillov dimension...), there is an exception (contrary usage) that for some (a few) quantum is any noncommutative, even _very_ noncommutative. Isn't that what has been said ? You are free to rephrase it. As far as preambles, I think they make sense once an entry/page grows beyond a single scroll; otherwise the compact version I find easier to edit and read in early development. Of course it is welcome to learn how to format it eventually, I am on the way to get used to it. Thank you.

   Large noncommutative algebras (say free associative algebras and alike) are typically not called quantum. Nevertheless, few authors view any noncommutative associative algebra as quantum.

   I do not understand where is a confusion. I see the two sentences as about quite the unlike usages of the term. Few/a few means in my understanding not many/only several. While for most people quantum is close to commutative (q-deformations, Noetherian, finite Gelfand-Kirillov dimension…), there is an exception (contrary usage) that for some (a few) quantum is any noncommutative, even very noncommutative. Isn’t that what has been said ?

   You are free to rephrase it.

   As far as preambles, I think they make sense once an entry/page grows beyond a single scroll; otherwise the compact version I find easier to edit and read in early development. Of course it is welcome to learn how to format it eventually, I am on the way to get used to it. Thank you.