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edit approved Sep 27, 2015 at 19:59
LSpice
edit approved Sep 27, 2015 at 19:59
LSpice
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You will find what you describe in the first reference. This describes how the Bernouilli numbers arise when studying the universal enveloping algebra. I have seen unpublished notes on this from a talk by Kostant in the '70s. This is a strong form of the PBW theorem and is closer to Poincare's result. This is discussed in the second reference. This is an early version of universal quantisation.

MR2301242MR2301242 (2008d:17015) Durov, Nikolai ; Meljanac, Stjepan ; Samsarov, Andjelo ; Škoda, Zoran . A universal formula for representing Lie algebra generators as formal power series with coefficients in the Weyl algebraA universal formula for representing Lie algebra generators as formal power series with coefficients in the Weyl algebra. J. Algebra 309 (2007), no. 1, 318--359.

MR1793103MR1793103 (2001f:01039) Ton-That, Tuong ; Tran, Thai-Duong . Poincaré's proof of the so-called Birkhoff-Witt theoremPoincaré's proof of the so-called Birkhoff-Witt theorem. Rev. Histoire Math. 5 (1999), no. 2, 249--284 (2000).

You will find what you describe in the first reference. This describes how the Bernouilli numbers arise when studying the universal enveloping algebra. I have seen unpublished notes on this from a talk by Kostant in the '70s. This is a strong form of the PBW theorem and is closer to Poincare's result. This is discussed in the second reference. This is an early version of universal quantisation.

MR2301242 (2008d:17015) Durov, Nikolai ; Meljanac, Stjepan ; Samsarov, Andjelo ; Škoda, Zoran . A universal formula for representing Lie algebra generators as formal power series with coefficients in the Weyl algebra. J. Algebra 309 (2007), no. 1, 318--359.

MR1793103 (2001f:01039) Ton-That, Tuong ; Tran, Thai-Duong . Poincaré's proof of the so-called Birkhoff-Witt theorem. Rev. Histoire Math. 5 (1999), no. 2, 249--284 (2000).

You will find what you describe in the first reference. This describes how the Bernouilli numbers arise when studying the universal enveloping algebra. I have seen unpublished notes on this from a talk by Kostant in the '70s. This is a strong form of the PBW theorem and is closer to Poincare's result. This is discussed in the second reference. This is an early version of universal quantisation.

MR2301242 (2008d:17015) Durov, Nikolai ; Meljanac, Stjepan ; Samsarov, Andjelo ; Škoda, Zoran . A universal formula for representing Lie algebra generators as formal power series with coefficients in the Weyl algebra. J. Algebra 309 (2007), no. 1, 318--359.

MR1793103 (2001f:01039) Ton-That, Tuong ; Tran, Thai-Duong . Poincaré's proof of the so-called Birkhoff-Witt theorem. Rev. Histoire Math. 5 (1999), no. 2, 249--284 (2000).

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Bruce Westbury
Bruce Westbury
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You will find what you describe in the first reference. This describes how the Bernouilli numbers arise when studying the universal enveloping algebra. I have seen unpublished notes on this from a talk by Kostant in the '70s. This is a strong form of the PBW theorem and is closer to Poincare's result. This is discussed in the second reference. This is an early version of universal quantisation.

MR2301242 (2008d:17015) Durov, Nikolai ; Meljanac, Stjepan ; Samsarov, Andjelo ; Škoda, Zoran . A universal formula for representing Lie algebra generators as formal power series with coefficients in the Weyl algebra. J. Algebra 309 (2007), no. 1, 318--359.

MR1793103 (2001f:01039) Ton-That, Tuong ; Tran, Thai-Duong . Poincaré's proof of the so-called Birkhoff-Witt theorem. Rev. Histoire Math. 5 (1999), no. 2, 249--284 (2000).