Journal of Lie Theory 35 (2025), No. 3, 573--582
Copyright Heldermann Verlag 2025
Multiplicative Lie Algebra Structures on the Semi-Direct Product of Groups
Deepak Pal
Indian Institute of Information Technology Allahabad, Prayagraj, India
deepakpal5797@gmail.com
Amit Kumar
Indian Institute of Information Technology Allahabad, Prayagraj, India
amitiiit007@gmail.com
Sumit Kumar Upadhyay
Indian Institute of Information Technology Allahabad, Prayagraj, India
upadhyaysumit365@gmail.com
Seema Kushwaha
Indian Institute of Information Technology Allahabad, Prayagraj, India
seema28k@gmail.com
We give a method to determine the multiplicative Lie algebra structures on the semi-direct product of groups under certain conditions. Consequently, we see that every multiplicative Lie algebra structure on the semi-direct product of two groups is completely determined by multiplicative Lie algebra structures on them.
Keywords: Multiplicative Lie algebra, direct product, semi-direct product.
MSC: 20D40, 20E34.
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