I re-edit my question for clarity.
I am looking for a citable reference about a "general" maths definition of spinors. I found many examples and definitions of spinors (books, papers, course notes, forums), but either they are restricted to particular situations or they are unclear.
Is a spinor:
(1) An element of the spin group, or
(2) An element of an (irreducible?) representation of the spin group, or
(3) An element of the space on which acts the spin group, or
(4) An element of a representation of the space on which acts the spin group, or
(5) Something else?
If one of (1-4) is correct, where can it be found (book, paper)?
Is there even a consensus about the definition?
If (5), a pointer to a general maths definition, preferably citable, is welcome.
Remark: The Wiki page does NOT answer the question: there are two contradictory definitions, none with citation. I had already read (https://en.wikipedia.org/wiki/Spinor) before sending my question. It is indicated that spinors are elements of a representation space of the spin group (case (2) of my question, but no reference given; and it does not match the case of Dirac spinors); some paragraphs later that the space of spinors is the fundamental representation of the Clifford algebra (no reference given), so a spinor is an element of this space. It is not the same definition: which one is correct? According to the talk of the Wiki page, no satisfactory definition emerges in the Wiki page.
So, I still look for a citation of a general definition, not only for a definition.
Thank you.