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In this paper, the origin of the generalized uncertainty principle (GUP) inan $M$-dimensional theory with Lie-$N$-algebra is considered. This theory whichwe name GLNA(Generalized Lie-$N$-Algebra)-theory can be reduced to $M$-theorywith $M=11$ and $N=3$. In this theory, at the beginning, two energies withpositive and negative signs are created from nothing and produce two types ofbranes with opposite quantum numbers and different numbers of timingdimensions. Coincidence with the birth of these branes, various derivatives ofbosonic fields emerge in the action of the system which produce the $r$ GUP forbosons. These branes interact with each other, compact and various derivativesof spinor fields appear in the action of the system which leads to the creationof the GUP for fermions. The previous predicted entropy of branes in the GUP iscorrected as due to the emergence of higher orders of derivatives and differentnumber of timing dimensions.

Birth of the GUP and its effect on the entropy of the Universe in Lie-$N$-algebra