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7:56 AM
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A: Tag management 2016

Najib IdrissiWhat is the tag differential-algebra for? Half of the questions seem to be about differential algebras (i.e. algebras over a field equipped with a differential), while the other half is about differential algebraic equations (i.e. equations that involve algebraic equations and differential equati...

I would expect the question in that tag to be about differential algebra and differential Galois theory. For example, this question is tagged according to this interpretation of the tag. — Martin Sleziak 51 secs ago
In mathematics, differential rings, differential fields, and differential algebras are rings, fields, and algebras equipped with finitely many derivations, which are unary functions that are linear and satisfy the Leibniz product rule. A natural example of a differential field is the field of rational functions C(t) in one variable, over the complex numbers, where the derivation is the differentiation with respect to t. Differential algebra refers also to the area of mathematics consisting in the study of these algebraic objects and their use for an algebraic study of the differential equations...
In mathematics, differential Galois theory studies the Galois groups of differential equations. == Overview == Whereas algebraic Galois theory studies extensions of algebraic fields, differential Galois theory studies extensions of differential fields, i.e. fields that are equipped with a derivation, D. Much of the theory of differential Galois theory is parallel to algebraic Galois theory. One difference between the two constructions is that the Galois groups in differential Galois theory tend to be matrix Lie groups, as compared with the finite groups often encountered in algebraic Galois theory...
"Differential algebra refers also to the area of mathematics consisting in the study of these algebraic objects and their use for an algebraic study of the differential equations. Differential algebra was introduced by Joseph Ritt."
In fact, I was unaware of other meanings of this term.
Oh. It seems that "differential algebra" is even more overloaded than I thought... Maybe "dg-algebras" (it's very rare for differential algebras not to be graded anyway), "differential-algebra" for differential Galois theory, and "diff-algebraic-eqns" for differential algebraic equations? — Najib Idrissi 1 min ago
 
8:32 AM
I do not know much about these topics. But if I read intro of the Wikipedia article I see that they first mention what differential algebras/fields/rings (as structures) are. Then they say that: "Differential algebra refers also to the area of mathematics consisting in the study of these algebraic objects and their use for an algebraic study of the differential equations." So based on this it seems that questions about differential algebras (as objects) and questions from differential algebra (as an area) could be in the same tag. — Martin Sleziak 1 min ago
 
 
5 hours later…
1:32 PM
Well my concern is that people who are interested in DGAs in the context of algebraic topology / homological algebra are often not very interested in differential equations, while people interested in differential equations are probably not very interested in minimal models, derived functors, dg-categories and whatnot. It takes a completely different skillset to answer these two questions: math.stackexchange.com/q/295387 math.stackexchange.com/q/1749579 (I can answer the first, but I hardly understand what the second is about, for example). — Najib Idrissi 4 hours ago
 

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