Geodesic
Minimum deformations of commutative algebra and linear group $GL(n)$
Teoretičeskaâ i matematičeskaâ fizika, Tome 95 (1993) no. 3, pp. 403-417 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the algebra of formal series $M_q(x^i)$, the relations of generalized commutativity that preserve the tensor $I_q$ grading and depend on parameters $q(i,k)$ are considered. A norm of the differential calculus on $M_q$ consistent with the $I_q$ grading is chosen. A new construction of a symmetrized tensor product of algebras of the type $M_q(x^i)$ and a corresponding definition of the minimally deformed linear group $QGL(n)$ and Lie algebra $qgl(n)$ are proposed. A study is made of the connection of $QGL(n)$ and $qgl(n)$ with the special matrix algebra $\operatorname {Mat}(n,Q)$, which consists of matrices with noncommuting elements. The deformed determinant in the algebra $\operatorname {Mat}(n,Q)$ is defined. The exponential mapping in the algebra $\operatorname {Mat}(n,Q)$ is considered on the basis of the Campbell–Hausdorff formula. 
@article{TMF_1993_95_3_a0,
     author = {B. M. Zupnik},
     title = {Minimum deformations of commutative algebra and linear group $GL(n)$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {403--417},
     year = {1993},
     volume = {95},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1993_95_3_a0/}
}
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B. M. Zupnik. Minimum deformations of commutative algebra and linear group $GL(n)$. Teoretičeskaâ i matematičeskaâ fizika, Tome 95 (1993) no. 3, pp. 403-417. http://geodesic.mathdoc.fr/item/TMF_1993_95_3_a0/

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